ASPECTS OF DEFLECTION BASIN PARAMETERS USED IN A MECHANISTIC
ASPECTS OF DEFLECTION BASIN
PARAMETERS USED IN A MECHANISTIC
REHABILITATION DESIGN PROCEDURE FOR
FLEXIBLE PAVEMENTS IN SOUTH AFRICA
HORAK, E
PhD (Civil Engineering)
University of Pretoria
1987
© U n i i v e r r s i i t t y o f f P r r e t o r r i a
MEASUREMENT AND DATA PROCESSING OF DEFLECTION BASINS IN
SOUTH AFRICA
ANALYSIS OF DEFLECTION BASINS MEASURED DURING ACCELERATED
TESTING
LITERATURE SURVEY ON MATERIAL CHARACTERIZATION AND
STRUCTURAL ANALYSIS USING DEFLECTION BASINS
EFFECTIVE ELASTIC MODULI DETERMINED FROM ROAD SURFACE
DEFLECTOMETER MEASUREMENTS
RELATIONSHIPS BETWEEN DISTRESS DETERMINANTS AND
DEFLECTION BASIN P~lETERS: A LITERATURE SURVEY
RELATIONSHIPS BETWEEN DEFLECTION BASIN PARAMETERS AND
DISTRESS DETERMINANTS FOR TYPICAL SOUTH AFRICAN PAVEMENTS
PROPOSED USE OF DEFLECTION BASIN MEASUREMENTS IN THE
MECIDl~ISTIC REHABILITATION DESIGN OF FLEXIBLE PAVEMENTS
CRACK MOVEMENT CALCULATIONS WITH DEFLECTION BASIN
MEASUREMENTS ON N4/ 3
ASPECTS OF DEFLECTION BASIN PARAMETERS USED IN A
MECHANISTIC REHABILITATION DESIGN PROCEDURE FOR FLEXIBLE
PAVEMENTS IN SOUTH AFRICA.
CIVIL ENGINEERING
PHILOSOPHIAE DOCTOR ( CIVIL ENGINEERING )
The nondestructive measurement of deflection basins has come a long way from measuring only maximum deflection or radius of curvature and using empirical relationships in rehabilitation design.
New equipment was developed worldwide and analysis techniques moved towards utilising the full deflection basin in fundamental analysis procedures.
This author addressed the problem of a proper description of the full deflection basin by doing a detailed literature survey on this subject.
Various deflection basin parameters that describe the deflection basin are listed, as well as the various measuring apparatus related to them.
The apparatus are all discussed in detail and related to the equipment available in South Africa.
The measurement of deflection basins with the road surface deflectometer
(RSD) under accelerated testing with the fleet of heavy vehicle simulators (HVSs) are described in detail.
An improved data manipulation procedure is proposed which simplifies the calculation of all the deflection basin parameters found in literature.
Various models to fit the measured deflection basins are also investigated in an effort to describe the deflection basin in full too.
The measured deflection basin parameters of a bitumen, granular, cemented and light structured granular base pavement are discussed in detail as being tested with the fleet of HVS's.
It is shown how the deflection basin parameters reflect the structural capacity of the various layers and behaviour states. A more accurate description of the behaviour states is made possible with the proposal of ranges for the various behaviour states for these deflection basins selected.
A literature study was carried out to investigate the various analysis procedures that use measured deflection basins as basic input in the characterization of materials.
On the basis of this study. linear elastic programmes were used to calculate effective elastic moduli for each pavement layer. using measured deflection basins as input.
The possibility to relate typical distress determinants to measured deflection basins were investigated in the literature.
Based on this.
typical South African flexible pavement structures were analysed mechanistically and typical design curves were established for typical bitumen and granular base pavements.
The effect of overlays were investigated too. resulting in typical overlay design curves.
In the final chapter the author endeavours to summarise the research by indicating how deflection basins can be measured and enhance the South
African mechanistic rehabiltation design process.
Only the latter rehabilitation design procedure is discussed with specific reference to the enhancement of the behaviour state identification.
material characterization.
analysis procedure and rehabilitation design with measured deflection basin parameters.
The author ends off by giving an indication of the future research need in this field of deflection basins.
ASPEKTE VAN DEFLEKSIEKOMPARAMETERS GEBRUIK IN 'N MEGA
NISTIESE REHABILITASIEONTWERPPROSEDURE VIR BUIGBARE
PLAVEISELS IN SUIDAFRIKA.
SIVIELE INGENIEURSWESE
PHILOSOPHIAE DOKTOR ( SIVIELE INGENIEURSWESE )
Die niedestruktiewe meting van defleksiekomme het 'n lang pad gevorder vanaf die meting van slegs maksimum defleksie of krommingstraal en die gebruik van empiriese verbande in rehabilitasieontwerp.
Nuwe toerusting is wereldwyd ontwikkel en analise tegnieke het in die rigting van die gebruik van die hele defleksiekom in meer fundamentele analiseprosedures beweeg.
Hierdie outeur spreek die probleem van die volledige beskrywing van die defleksiekom aan deur 'n diepgaande literatuurstudie oor hierdie onderwerp te doen. Verskeie defleksiekomparameters wat die defleksiekom beskryf.
word gelys.
sowel as die onderskeie apparate wat daarmee verband hou. Hierdie apparate word almal in detail bespreek en in verband gebring met die toerusting wat in SuidAfrika beskikbaar is.
Die meting van defleksiekomme met die padoppervlaktedeflektometer (POD) onder versnelde toetsing met die vloot van swaarvoertuignabootsers
(SVN'e) is in detail beskryf.
'n Verbeterde datamanipulasieprosedure is voorgestel wat die berekening van al die defleksiekomparameters vereenvoudig soos gevind in die literatuur.
Verskeie modelle wat gebruik is om die gemete defleksiekom te pas. is ondersoek in 'n poging om die defleksiekom ten volle te beskryf.
Die gemete defleksiekomparameters van 'n bitumen.
gebreekte klip.
gesementeerde en ligte struktuur korrelkroonlaagplaveisel is in detail bespreek soos getoets met die vloot SVN'e. Daar is getoon hoe die defleksiekomparameters die strukturele kapasiteit van die onderskeie lae en gedragstoestande reflekteer.
'n Meer akkurate beskrywing van die gedragstoestande is moontlik gemaak deur die daarstelling van grense vir die verskillende gedragstate van die gesellekteerde defleksiekomparameters.
'n Literatuurstudie is gedoen om die verskillende analiseprosedures wat van defleksiekomparameters as basiese inset gebruik maak, in die karakterisering van materiale, te ondersoek.
Op grond van hierdie studie is daar ook gepoog om gebruik te maak van linieer elastiese programme om effektiewe elastiese moduli te bereken, vir elke plaveisellaag, vanaf gemete defleksiekomme.
Die moontlikheid om determinante vir oorspannendheid direk aan gemete defleksiekomparameters te kan koppel, is in die literatuur nagevors.
Op hierdie trant is daar toe tipiese SuidAfrikaanse soepel plaveiselstrukture meganisties ontleed en sogenaamde ontwerpkurwes daargestel vir tipiese bitumenen korrelkroonlaagplaveisels.
Die invloed van herdeklae is ook ondersoek en tipiese herdeklaag ontwerpkurwes is daargestel.
In die finale hoofstuk poog die skrywer om die navorsing op te som deur aan te dui hoe defleksiekomme gemeet kan word en die SuidAfrikaanse meganistiese rehabilitasie ontwerpprosedure kan versterk.
Slegs laasgenoemde rehabilitasie ontwerpprosedure is bespreekmet spesifieke verwysing na hoe gemete defleksiekomparameters die gedragstoestande kan identifiseer, materiale karakteriseer, die analise prosedure en rehabilitasie ontwerp kan versterk.
Die outeur eindig deur aan te dui wat die navorsingsbehoefte in die toekoms is ten opsigte van defleksiekomme.
I thank my friend and Lord Jesus Christ for setting me free to become the person He wants me to be. May this thesis also contribute to His gloryl
The Chief Director of the NITRR, Mr R N Walker, is thanked for the permission to use this research work done at the Institute in this thesis.
I thank Dr Charles Freeme, former group head of the Pavement Engineering
Group, for his enthusiastic support and motivation by excellent example.
In the same breath I would like to thank Professor Carl Monismith from
U.C. Berkeley, who initiated my interest in this field.
I thank the whole former Pavement Engineering Group for their kind cooperation and interest.
Rassie Otte is singled out for his perseverance and hard work on the computer.
A special word of thanks to
Rolette Sutton for her meticulous editing.
The typing done by the typing pool is highly appreciated.
I would like to thank my wife Mariana for her loving support, and
Helene, Emile, Eduard and Ane for enduring the moods.
Last of all I would like to thank my parents, Markie and Bets, for their support and interest over the years.
Markie, I know you would have been proud I
CH.APTER 1
A LITERATURE SURVEY ON DEFLECTION BASIN MEASUREMENTS
1
INTRODUCTION
2
DEFLECTION BASIN PARAMETERS
2.1
2.2
Review of parameters
Evaluation of parameters
3 DEFLECTION MEASURING
3.1
Review of devices and methods
3.2
Evaluation of devices
3.3
Correlations between devices
4 CONCLUSIONS AND RECOMMENDATIONS
PAGE
1.2
1.5
1.5
1.7
I. 19
I. 19
I. 21
I. 31
I. 32
In the development of fundamental methods of pavement evaluation by means of deflection measurements it is imperative that an accurate description of the deflection basin be given.
In the majority of analysis procedures only the maximum surface deflection (<5) is o measured (Epps and Hicks, 1982).
Owing to the empirical nature of analysis techniques in the past, a more detailed description of the deflection basin has been neglected.
In Figure 1.1 it can be seen that the same maximum deflection value, <5 , can be measured on two o pavements with totally different deflection basins and structural response characteristics.
Whitcomb (1982) even concludes from various examples of this phenomenon that " ....resilient moduli for layers in a pavement system cannot be back calculated using maximum surface deflection alone".
In their analysis of Alascan highways during the spring thaw period Stubstad et al. (1983) show that the same maximum deflection value could lead to wrong assumptions of thaw depth and resulting damage potential.
It is only by looking at the whole deflection basin that preventative predictions of thaw depth can be made.
Although South Africa does not have pavement distress due to thaw as in North America, it is significant that the whole deflection basin can be used to indicate a change of state.
Paterson et al. (1974) states that when a pavement deflects under a load, the influence of the load extends over a certain area.
In one dimension and for one depth this can be regarded as a deflection profile or influence line of, say, the surface.
In two dimensions the deflection at any depth is given by an influence surface.
The shape of the influence surface reflects the structure of the pavement.
In Figure 1.2
the typical deflection profiles for a uniform circular load and the more complex shapes of aual wheel single axle loads and how front and back axles influence each other
,are shown.
The depth profile of the deflection closely reflects the stiffness depth profile of the pavement in relation to the relevant stress levels.
This is best swnmarised by the Technical Committee Report of the
XVII World Road Congress (Permanent International Association of
I
DEFLECTION DIFFERENCE AT OFFSET
I r
Illustration of the same maximum deflection for two different deflection basins.
FIGURE 1.1
DEFLECTION' BASIN ILLUSTRATION.
, o
"'"
8
REAR WHEELS
FRONT WHEEL b) UNDER A SINGLE REAR AXLE DUAL WHEEL
TRUCK
TYPICAL
FIGURE 1.2
SHAPES OF DEFLECTION INFLUENCE
LI NES (Dehlen ,1962 b)
Road Congresses ,1983).
"There are obvious attractions in making maximum use of the information that can, in principle, be obtained by detailed evaluation of the deflected shape as it obviates or reduces the need for assumptions about, or measurement of, properties of pavement materials."
This introductory discussion clearly indicate that there is a need for the measurement and interpretation of the full deflection basin.
As will be discussed in later chapters, in South Africa the full deflection basin is measured, but the analysis historically focussed on the small area surrounding maximum deflection. In order to make better use of the full deflection basin , a literature survey was conducted. This literature survey covers the work done overseas with other measuring equipment description methods of the full deflection basin , evaluation of various deflection basin parameters and devices.
In order to bring it in line with the South African scene , all these discussions are related to the practice here .
Recommendations are made by this author to enhance the current practice and use of South African devices and deflection basin description.
Surface deflections are generally measured by sensor(s) of various kinds located in a fixed line and normally at a fixed distance relative to the centriod of the load area.
Deflection basin parameters differ in their relation to the measuring device and degree to which they describe the essential features of the deflection basin.
In Table 1.1 a summary is given of the parameters, formulae, test method or device normally associated with it and at least one reference.
It is suggested that the foldin of Table 1.1 at the back be folded out to ensure ease of reading as exhaustive reference will be made to the various deflection basin parameters in the sections to follow, as well as the chapters to follow.
Parameter
I. Maximum deflection
2. Radius of curvature
8
0
Formula
R= r 2
280(80/8r
r = 127 mm
1)
Measuring device
Curvaturemeter
Reference
Benkelman beam
KennedYl et at
Lacroix deflectograp, Asphalt Institute( 197
Dehlen (1962 a)
3. Spreadability
S=
[(80+81 +8
2
+8;y/5]100
80
8
1 ••••
83 spaced 305 mm
Dyna f lect Vaswani
(1971)
4. Area
5. Shape factors
A = 6 [I
+
2
(8/8~ +
2
(8
2
180)
+
83/80 ]
F, = (80  82)
I 8
1
F 2
=
(8
I 
83)
I
82
6. Surface curvature index
SCI
=
808 r i r = 305 mm or r = 500 mm where
7. Base curvature
BCI index
=
8610 891~
8. Base damage index
BD!
= 8305  8610
9. Deflection ratio
10.Bending
Index
II. Slope of deflection
12.Tangent
slope
13.Radius of influence
Falling weight
Hoffman and deflectometedFWD)
Thompson (1981)
FWD
Hoff man and.
Thompson (1981)
Benkelman beam
Anderson (1977)
Road rater
Kilareskilat a1.(1982)
FWD
Molenaar (1982)
Road rater
Kilareskilet al.(/982)
Road rater
Kilareski,et aL( 1982
Or
=
8 r 180 where
FWD ar~
80/2
Claessen and
Ditmarsch (1977)
BI
• 8 la a • Deflection where basin
SD= tan
1
(80 
8r)/r
where r = 610 mm
ST
=
(So 
8 r)
I
r where r is determined by a polynomial function
RI =R'/80 where
R' is the distance from
80 to where basin is tangent to horizon.
Benkelman beam
H veem (1955)
Benkelman beam
Kung (1967)
Benkelman beam
University of
FWD
Dundee (1.980)
Ford and
Bissett ( 1962)
The first two parameters listed in Table 1.1 are the traditional maximum deflection and radius of curvature. Their formulas show that only the small area surrounding maximum deflection
(positive curvature) is utilized. The spreadibilty (5) and area
(A) parameters obviously cover the full deflection basin.
Parameters such as the shape factors (F1 and F2), surface curvature index (5CI), base damage index (BDI), base curvature index (BCI), slope of deflection (5D) and tangent slope (5T) also cover more than only part of the area of positive curvature near the load. In fact some of the aforementioned parameters try to describe either the area of positive curvature or the area of reverse curvature or the important area surrounding the point of inflection where the positive curvature changes to that of the reverse curvature.
The other parameters not mentioned, do describe the deflection basin better than maximum deflection and radius of curvature, but it is not clear in which area of the deflection basin they fall with their description.
The Technical Committee Report on flexible Roads of the XVII
World Road Congress (Permanent International Association of Road
Congresses, 1983) states; "The transient displacement or deflection of the road surface represents the sum of all the vertical strains in the pavement and subgrade and remains the most widely used measurement of structural condition.
Its advantages are, the relative simplicity of the measurements, the large amount of experimental data that already exists and the strong correlation found between deflection and overall performance in well defined conditions.
It is however not very responsive to changes in the stiffness of upper pavement layers and is not a unique measurement of performance on all types of pavement."
A sensitivity analysis done at the University of Dundee (1980) incorporated most of the parameters listed in Table 1.1.
A threelayered pavement system was analysed.
All the structural parameters were varied.
The sensitivity analysis was done by
Irrespective of the technique or measuring device, the parameters, bending index (BI) and radius of influence (RI) are difficult to determine.
This is due to the fact that the length of the deflection basin is normally too long to measure accurately in situ.
The value of maximum deflection (0 ) was o found to be unreliable when used alone owing to the difference in pavement conditions.
This confirms the illustration in
Figure 1.1 and conclusion by Whitcomb (1982) in Section 1.
Radius of curvature parameter (R) showed a high sensitivity to most changes in the pavement structural parameters, but was insensitive to subgrade elastic modulus.
The deflection ratio
(Q or Qr) and spreadability (S) showed even less sensitivity to changes in the other structural parameters.
Contrary to this conclusion Koole (1979) reports that the parameter Q is a reliable parameter.
The inconsistency seems to stem from the lack of adherence to Koole's (1979) precondition (0 :::0 in
.
r
0 determining Q. It seems that using a fixed value of 0r=0610' as in this analysis done by the University of Dundee (1980), can result in the recorded insensitivity to changes in the pavement structural parameters.
If it is taken into consideration that
.this parameter was developed for a specific type of pavement structure, it is to be expected that variances in structure will definitely influence its sensitivity.
Rohlf et al.
(1985) indicate that spreadability (S) is an indication of the ratio of the surface layer to support layer strengths.
In this sensitivity analysis by the University of Dundee (1980) the slope of deflection (SD) and tangent slope (ST) have shown a high sensitivity to changes in the pavement structural parameters.
It is concluded, though, that the slope of deflection
(SD) may have the same unreliability as the maximum deflection
(0
0) when used alone.
The reason for this is that, as illustrated in Table 1.1, a fixed value of 0 =0610 is used.
The r tangent slope, on the other hand, makes use of a polynomial
function to describe the deflection basin and form the basis for the selection of 6 unambiguously.
r
Dehlen (1962b) also observed that R is dependent mainly on the moduli of the upper layers of construction.
and very little on those of the materials at depth.
He states that; "The radius of curvature of a road surface under a given vehicle is dependent mainly on the
Young
I s moduli of the materials in the base and subbase;...
"He also observed that R is dependent to a considerable degree on tyre pressure and only to a lesser degree on the wheel load while 6 is dependent on wheel load and little on tyre pressure.
o
Hoffman and Thompson (1981) developed the area (A) parameter from work done by Vaswani (1971).
It is obviously related to the spreadability (S) parameter and an attempt to incorporate the full deflection basin.
The surface curvature index (SCI) indicates the strength of the upper portion of a pavement according to an analysis of standard pavement structures in the State of Victoria, Australia by
Anderson (1977).
Generally in these pavement structures, as in the dry regions of South Africa, rather thin
(±
50 mm) asphalt surfacing layers are used.
In Anderson's (1977) study, maximum deflection (6 ) was used simultaneously to describe the response o of the lower portion of pavements successfully.
Kilareski et al.
(1982) state that the base curvature index
(BCI) indicates the strength of the lower portion of the pavement system.
The basis for these statements concerning SCI and BCI can be seen in Figures 1.3 and 1.4 where the related structural parameters are varied.
It can be seen in Figure 1.3
that a difference in deflection at 0 and 305 mm (SCI) will reflect the change in base elastic modulus.
In Figure 1.4 the difference in deflection at 610 mm and 915 mm (BCI) will reflect the change in subgrade elastic modulus.
The Technical Committee Report on flexible roads of the XVII
World Road Congress (Permanent International Association of Road
Congresses, 1983) concludes on the deflected shape; "The
200 tu
I.LJ
..J
L&
I.LJ
0
I
'It
E
E


0 z
0
175
150
125
I.LJ
U
<
L&
0::
::::>
(/)
..J
<
o::
I.LJ
>
100
75
50
E,. 6900 MPa
E, • 3450 MPa
El • 1380 MPa
E
1
=
BASE ELASTIC
MODULUS
25 o
200 400 600 800
DISTANCE FROM LOADING CENTRE (mm)
FIGURE 1.3
VARIATION OF SURFACE
DEFLECTION BASIN WITH
SURFACE MODULUS, E
I
(Kilareski, et 01.,1982)
FIGURE 1.4
VARIATION OF SURFACE DEFLECTION
BASIN WITH SUBGRADE MODULUS,E
4
( K i lareski, et aI., 1982)
deflected sensitive shape near the point of maximum deflection to changes in upper pavement layers and relatively is unaffected by the subgrade.
Deflection levels and their rate of change further from the maximumhave been related to the stiffness of lower pavement layers and the subgrade."
Very interesting deflection basin information parameters is relate available to on increase how the in various number of standard axle repetitions.
Kilareski et al.
(1982) produced the typical results of deflection versus number of equivalent axle repetitions as shown in Figure 1.5.
SCI (difference between
Sensors
1 and 2) and the
4) are virtually
BCI (difference between Sensors 3 and constant with the increase in number of standard axle repetitions.
From this follows the need for the development of the base damage index (BDI) which is the difference between Sensors 2 and 3).
The values of the BDI change with the increase in repetitions results from work done of standard by Molenaar (1983); axles.
in
Figure spite of
1.6
the difference in measuring technique and device (see Table
1.1) it shows considerable support for this approach of relating surface curvature index (SCI) to the repetitions of the standard axles.
Rohlf et a10 (1985) did a multivariate
Dynaflect deflection data.
A relationship analysis of pavement between Dynaflect deflections and pavement temperature, cumulative traffic loading for subgrade a number of moisture, different and pavement sections was developed.
measurement is illustrated
A typical Dynaflect deflection in Figure 1.7.
The major from this study is that the base thicknesses basin conclusion and base layer elastic tions.
moduli
The had first significant sensor related to the base thickness.
effects deflection on the sensor
(maximum) was deflecdirectly
Tam (1985) ana lysed three, fourand fivelayered structures and determined how the variation of structural pavement inputs affected the deflection basin.
Figure 1.8
summarizes relative importance of the effect of varying the stiffnesses the of
z

1,50
Iu l.LJ
..J
l.L
l.LJ
0
0 z
0
0..
0

1,00
0,50
0
TEST SECTION
1c
SENSORS SPACED AT 305 mm
3
4
0,5 1,0 1,5
(EAL Millions)
2,0
2,5
FIGURE 1.5
CORRECTED ROAD RATER SURFACE
DEFLECTIONS VS. ISKIP (SO kN)
EQUIVALENT SINGLE  AXLE LOAD
(Kilareski,et
01., 19S2)
3,0
10
7
(j)
X
~
~
Z w
~

0 w l1..
0 a::: w
CD
::
::> z
10
6
10~
10
4
FIGURE 1.6
EXAMPLE OF A PAVEMENT DESIGN
CURVE BASED ON THE SURFACE
CURVATURE INDEX (SC I) (Molenoor,1983)
20"
12"
LOADING
WHEELS
ORIGINAL
SURFACi
48"
WI
(OMO)
~
•...•.
"
"
"
.......
....••..

W4
W2
W3
seI
'DEFLECTED
SURFACE
DYNAFLECT
FIGU RE I. 7
DEFLECTION BASIN (Rohlf, at 01.,1985)
DISTANCE FROM LOAD CENTRECm) o
0,3 0,6 0,9 1,2 1,5 1,8
STIFF
SUBGRAOE
Ewe: 4000
EB
:10000
,><,
E
SG :
110
""
Ewe: 4000
EB
: 10000
JX<
E
SG:
30
M<
Ewe: 4000
E
B :
14000
A<
E
SG:
50
,"",
Ewe: 4000
E
B :
4000
>x< ,,,,,
E
SG :
50
All units in MPa for stiffness modulus,E used in each layer
FIGURE 1.8
RELATIONSHIP BETWEEN VARIATION OF
STIFFNESS MODULI IN BASE LAYER AND
SUBGRADE ( Tam, 1985)
the base layer and the subgrade in a threelayered pavement structure.
The main conclusions from the Tam study on threelayered pavement structures are as follows:
(a) The variation of base layer thickness had the greatest influence on maximum deflection (<5 ) and spreadability (S).
This was o followed by the subgrade stiffness and base stiffness.
Spreadability (S) had seven deflections incorporated in the calculation instead of the normal five (see Table 1.1).
(b) As the subgrade stiffness increases (decreases), maximum deflection (<5 ) and spreadability (S) decrease (increase) (see o
Figure 1.8).
(c) The increase (decrease) in magnitudes of pavement structural parameters reduces (increases) maximum increases (reduces) spreadability (S).
deflection
(<5), o but
In Figure'l.9 the typical fourlayered pavement system, as analysed as reference system by Tam (1985), is shown.
The spreadability (S) and maximum deflection (<5 ) was normalized by a o ratio to the value of the reference structure.
The main conclusions here were the same as for the threelayered pavement system regarding the influence of the base and subgrade.
It also showed that maximum deflection (<5 ) and spreadability (S) o were hardly affected by the change of subbase parameters at all.
The implications are that the actual stiffnesses of the subbase will be difficult to determine with accuracy in evaluating existing pavement conditions and high accuracy on subbase thicknesses will not be a prerequisite for analysing such pavements.
In the South African context this is a typical granular subbase pavement.
In Figure 1.10
the typical reference fivelayered pavement structure is shown.
In this case a cemented subbase in the precrack phase was analysed.
The sensitivity analysis on maximum deflection (0 ) and spreadability (S) are also shown.
o
REFERENCESTRUCTURE
Ewc=4000 MPa, u = 0, 4
Ee = 1000 MPa, u =0,4
l hwc= 40mm
1,·2000'0' hse=200mm Ese = 100 MPa, u = 0,3
1::<.":
/A
ESG= 50 MPa, u =0,4
80
= 431,.,.m,
S = 0,678
0:
LU
I
LU
:E
<X
0:
<X
Q.
LU
U
Z
LU
0:
IJJ lL.
LU
0:
2,5
2,0
J:LU
10:
::>
31
og
0: t:il
0:CJ)
1,5
1,0
0,5
•
~~ hse Ese
Ee
0
0,4 0,6 0,8 1,0 1,2
1,4
1,6
MAX. DEFLECTION
RATIO
2,5
1,5
1,0
0,5
0
0,8
Ee
•
V
h/1E
SB
1,0 1,2
SPREADABILI TY
RATIO
FI GURE 1.9
RELATIVE SENSITIVITY OF PARAMETERS OF SUBBASE LAYER
(Tam
1
1985)
REFERENCESTRUCTURE
.1.
Ewc=4000MPa, u=0,4 hwc=40mm
Eee =IOOOOMPa, u=O,4 hec=15Omm hRe=200mm hse=200mm
+
\
\
'+
• E ee
~ hRe }LEA: MIX c
ER8 ASPHALT
+
E
SG o
0,6 0,8 1,0 1,2 1,4 1,6
MAX. DEFLECTION RATIO
1,0 1,2
SPREADA81L1TY RATIO
FIGURE 1.10
RELATIVE SENSITIVITY OF PARAMETERS OF LEAN MIX AND
ASPHALT BASE LAYER (Tam ,1985)
The main conclusion here was that deflections are sensitive to the variation of thickness of the lean concrete subbase and the asphalt base.
Hence, it is important to know what their actual thicknesses are to enable one to evaluate the condition of the existing pavements with confidence.
Pavement deflection devices made their appearance in 1938 in
California.
The California Division of Highways installed the
General Electric Travel Gauge statewide in that year.
This type of device developed evolutionarily.
This process was enhanced by the use of these devices at test tracks such as those at Brighton and Stockton, and at WASHO and AASHO road tests.
(Whitcomb, 1982).
Since then the use of nondestructive deflection measuring devices has become standard practice world wide.
a) b) c) d) e) increase the testing production rate increase the accuracy of measurements simulate moving traffic loads in terms of magnitude of load, shape and equivalent time of loading provide simplicity of operation and interpretation of results reduce the cost of testing.
Most deflection testing equipment can be classified by loading mode.
Generally these devices fall into three main groups: static or slowmoving wheel devices, steadystate vibratory devices and impulse or falling weight devices.
Table 1.2 lists a brief summary of the devices as classified by Monismith
(1979) .
Whitcomb (1982) mentions several other sophisticated devices.
The moving vehicle device and accelerometers which need instrument installation in the pavement, cannot strictly be regarded as nondestructive deflection basin testing.
Others mentioned are a deflection beam measuring perpendicular to a passing vehicle, laser technology and new techniques in photogrammetry.
The road surface deflectometer (RSD) and multidepth deflectometer (MDD) developed in South Africa for use with the Heavy
Vehicle Simulator (HVS) described by Freeme et al.
(1981) can also be seen as recent developments.
Strictly speaking the MDD is a destructive deflection measuring device in terms of its installation procedure.
Method by which load is applied
Slowmoving
Wheel
Vibratory load
Falling weight
Organization by which used
(Examples)
Asphalt Institute, College
Park, Maryland
NITRR. CSIR, South Africa
Road surface deflectometer
(RSD)
Travelling deflectograph
Light vibrators, e.g.
Road raters and
Dynaflect
California Department of
Transportation
Transport and Road Research
Laboratory.
Great Britain.
National Institute for Transport and Road Research.
S.A.
Main Roads Department, New
South Wales, Australia,
LCPC. France
LCPC, France.
States: California,
Kentucky, Louisiana, Utah.
Federal Highway Administration
U.S. Army Corps of Engineers,
Waterways Experiment Station
Falling weight deflectometer
(FWD)
Whitcomb (1982) states that criteria for determining the "best" deflection testing device from a technical standpoint are difficult to describe.
Various comparative studies have been made.
In his comprehensive study Bush (1980) compared the operational characteristics (for example ease, speed and manpower requirements), costs (initial and operating), accuracy, reproducability of measurements and depth of influence of
Relative values of 1 to 10 were used with 1 being the most desirable and 10 the least.
The results of this table clearly indicate a preference for the Dynaflect Model 2008, Road Raters and FWD.
The most comprehensive recent study comparing nondestructive testing (NDT) devices and methods for use in the overlay design of flexible pavements is that by the Federal Highway Administration (FHWA, 1984).
User comments on the various devices were collected from allover the world.
The following factors were considered:
(a) time in service
(b) crew size
(c) professional qualifications of crew
(d) number of test points per day
(e) cost per test point
(f) maintenance costs
(g) traffic control costs
(h) data recording methods
(i) data storage
(j) towing vehicle.
variation is apparently due to a difference in user rather than equipment.
It does, however, give a good guide.
It is obvious that the device that comes out best will depend on which factor is selected.
Another comparative study, also from the FHWA (1984) study, is shown in Table 1.5.
It covers a wide range of criteria and the final result indicates that the FWD is favoured.
The Road
Raters and even the Dynaflect are not far behind in this rating.
This emphasizes the fact that each device has its strong and weak points.
A few relevant conclusions from this study by the FHWA (1984) are as follows:
(a) The Dynaflect, Road Raters and FWD are eqUipped to measure deflection basin parameters more quickly and efficiently than the static and automated beam devices;
Optional characteristics
Ease
Speed
Manpower
SUBTOTAL
Costs
Accuracy
Deflection
Force
SUBTOTAL
Transportability by cargo aircraft
Depth of influence
Suitability
TOTALS
6
6
6
18
Benkelman beam
6
6
3
6
1
7
Dynaflect
1
1
1
3
2
4
6
1
1
2
5
5
3
13
1
3
4
FWD
5
5
1
6
23
1
1
3
14
2
5
2
2
1
16
Model 400 Model 510 Model 2008 road rater road rater road rater
3 2
3
2
3
8
2
5
7
2
3
4
2
3
9
2
5
7
4
2
3
5
1
6
2
2
1
5
4
2
5
22
3
6
3
18
2
4
2
3
1
14
N w
SUMMARY OF SELECTED DATA REPORTED
ON VARIOUS NONDESTRUCTIVE TESTING
DEVICES
Deflection beam
Mean
Standard deviation
Oynaflect
Mean
Standard deviation
3 83
23
$
127
$
1,52
0 24 1,4 '$ 106
<$
0,99
<$
42 <$
262
'$ 12,50
1,8 234 14 '$ 88
0,5 130 5
<$
67
$
0,44 '$ 2242 '$ 408
$
0,21
$
I 950
$ 229
Falling weight deflectometer
Mean
Standard deviation
1,9 169 15,5
<$
262,5 1> 1,41
$
3250
$
363
0,2 65 0,9
$
237,5
<$
1,09
$
1750
<$
274
Road rater (all models)
Mean
Standard deviation
1,3 292 10
$
362 '$ 1,69 '$ 2075
$
176
0,4 86 2,5
$
178 '$ 1,17 '$ 2104 '$ 43
Travell ing deflectometer /defle cto graph
Mean
Standard deviation
22667
0 656
18,7'$
3,8 '$
278 $ 0,10 $3312'$
111 '$ 0,02 '$ 312
600
TABLE 1.5:COMBINED RATINGS REPORTED IN
LITERATURE (LARGER NUMBERS
INDICATE BETTER RATING)
Rating Criteria
Dynaflect RR 400B
RR2000
Cost per lane mile
Operator training
Actual load capability(5)
Design compatibility
9.5
10.0
Speed of operation ( 1)
7.5
Traffic Interference (1 )
7.5
Ease of data collection(2) 10.0
Ease of calibration (3)
Equipment versatility(4)
2.0
0
1.0
Combined rating
57.5
10.0
10.0
10.0
10.0
10.0
5.0
10.0
2.9
77.9
79.7
9.2
10.0
10.0
10.0
10.0
5.0
10.0
5.5
( I) Based on the theoretica I test program.
(2)
(3)
Assumes the recommended options.
Based on the time required for calibration.
(4) Based on ability to vary the applied load.
(5) Based on ability to produce a 10,000 lb. dual wheel load.
FWD
7.5
10.0
10.0
10.0
10.0
10.0
10.0
10.0
87.5
(b) The automated beam device, FWD and Road Rater model 2008
(c) can develop loads at, or near, normal design loads;
Load as well as deflection can easily be measured.
The
Road Raters and FWD are equipped to measure load as well as deflection;
(d) Devices capable of producing several load levels up to, or near, design loads can be used to determine the stress sensitivity of pavement systems, and
(e) Steady state dynamic devices, which use a relatively heavy static preload, change the stress state in the pavement before the testing.
The slowmoving wheel devices like the Benkelman beam and deflectographs may be seen as representing the first generation of measuring deVices; the vibratory and falling weight devices are more recent developments.
Of prime concern is the fact that the slowmoving devices are normally associated with a single measuring point, whereas the later generation measuring devices are increasingly able to describe the deflection basin.
This is normally achieved with the equally spaced measuring points away from the point of loading.
The development of the
RSD (Freeme et a1.
1981) and modification of the standard
Benkelman beam and Lacroix deflectograph (Anderson,
1977), which can produce a "continuous" plot of the deflection basin, overcome this disadvantage.
In general it can be stated that the more accurate the measuring device can measure the deflection basin, the better it is.
The curviameter can strictly be called a fast rolling wheel technique.
the XVII
The Technical
World Road
Committee Report
Congress on flexible
(Permanent roads
International of
Association of Road Congresses, 1983) described it as follows;
"The Curviameter carries a velocitysensitive transducer on an endless moving chain that places and replaces the transducer in advance of the loaded dual wheels of a lorry moving at 20'km/h.
Although the machine gives an increase in routecapacity rolling wheel techniques the derived deflections and curvatures of are of limited accuracy."
The slowmoving wheel devices generally measure deflection with a standard axle load.
Depending on the measuring technique of the wheel moving to or from the measuring point, deflections vary.
Although a lot can be said for these techniques can and devices simulating the actual moving wheel loads (more accurately), it must be remembered that the simulation is normally much slower than the real situation deformation come into play.
In this and effects regard like plastic
Whitcomb (1982) states that the input from the static commonly used bears little resemblance and to vibratory the input devices from an actual vehicle.
Molenaar and Koole (1982) mention that the low force levels of the light vibrators on predicted pavement behaviour are a cause for concern.
This concern is not only with respect to possible nonlinear behaviour of the pavement, but also with respect to errors in measurement, particularly measurements taken at the extremes of the deflection basin where deflections measured and normal variations of instruments are of the same magnitude.
The heavy vibrators described by the
Federal Aviation Administration (1979) have adequate loading force, but are mainly used to evaluate airfield pavements.
The FWDmeets all requirements for reliability, reproduction, accuracy, simulation of moving wheel loads and measuring the whole deflection basin and it does not alter the conditions of the pavement before loading (Whitcomb, 1982).
The FWDcan vary the force from 40 to 125 kN and will represent any loading
condition
Ditmarsch, 1977 and Koole,
I. 28 on a pavement or airfield
1979).
the FWDsimulated the influence of a heavy fastmoving wheel load on the maximumvalues of the deflections, stresses and strains in the pavement structure.
realistically (Claessen and
Ullidtz (1982) concludes that
In the study by the University of Dundee (1980) it is shown that when equipment measuring deflection with dual wheel loads is used, (for example the Benkelman beam), the maximum deflection is not located at the centroid of the loading area.
illustrated by the results of a typical analysis in Figure
This is
1.11.
Anderson (1977) also recognizes the importance of this phenomenon and noted that it might lead to wrong conclusions, particularly for relatively weak (thin) pavements.
He suggested that field performance should be calibrated with ana lysed pavements before being adopted in the design phase.
The former study recommended the use of a single wheel device and proved that deflections measured at the extremes of the loaded area did not significantly vary from deflections measured inside the loaded area.
Dehlen (1962b) also recognized this phenom~non of d (maximum) and R minimumbeing situated under the loaded area.
o
The transverse position also lead to the more severe curvature parameters measured of the deflection basin.
This is illustrated in Figure 1.12.
Dehlen (1962b) statesj "The longitudinal elongation observed in many chicken net crack patterns is, as has been pointed out by others, another indication that the factors giving rise to cracking are most severe in the transverse direction."
The Technical Committee Report of the XVII World Road Congress
(Permanent International Association of Road Congresses, 1983) states that interest in developing analytical linked more to stationary test techniques than design to methods is the rolling wheel techniques.
The light vibrators are obviously ideal for standard field work as Tables 1.3, 1.4 and 1.5 indicate.
In spite of the advantages of using the FWDmentioned earlier, Molenaar and Koole (1982) comment that, according to conclusions of a study group of the Dutch Study Centre for Road Construction, the
0,4 x
(m)
STRUCTURE 3.4
.".,." ,
~~
/"A.
x jm)
~
_~

..
~
7
.~
.
~
.,.
.""".

.
.
J.
4;'/
"r/
___________ 0,29 z (mm) _
WHEEL LOAD
AREA o m
ICl
"" o
U)
••••
V
I
V
I o
~
(m)
0,0
0,05

_.
0,1
0,15







.
...r'LOCUS OF MAX fY DEFLECTION
FIGURE 1.11
TRANSVERSE DEFLECTION PROFILES
(University of Dundee 11980)
~u ~b ~u
,030
11
,026
11
;032
11
Rtu
Rtb Rtu
155
1
90
1
125
1
20
INCHES
30
LL w
0
U)

z
0
W
J:
(,) z
l
(,)

,020
,040
30
,060
20
DEFLECTION
RADII
CURVATURE
SITE A
1
ROUTE 3/ I
FIGURE 1.12
TYPICAL EXAMPLE OF TRANSVERSE DEFLECTION
PATTERN BENEATH DUAL WHEELS (Dehlen, 1962 b)
.
w
0
I. 31
Lacroix deflectograph is more suitable for routine evaluations than the FWD.
The RSD developed in South Africa overcomes the normal problems experienced with a standard Benkelman beam concerning poor sampling frequency and testing in adverse weather conditions.
Owing to the limited length of any such beam device the problem of the beam supports being inside the deflection basin will not be eliminated completely.
This is particularly true of stiffer pavements where the deflection basin is broad.
The Technical Committee Report on flexible Roads of the XVII World Road Congress (Permanent International Association of Road Congresses, 1983) also concludes that; "Precision of measurement can be difficult when testing stiff pavements containing cemented layers and cracking in those layers can reduce the significance of measurements of the deflected shape."
There are numerous references in the literature to the correlation of deflections obtained with the different devices.
Generally the newer generation measuring devices are correlated with the older generation devices like the Benkelman beam.
Whitcomb (1982) records relationships between the Road rater.
Dynaflect and Benkelman beam or travelling deflectometer.
Hoyinck, et ale (1982) even correlate Lacroix deflectograph and
Benkelman beam deflections measured with different techniques.
The reason for the correlations is that one type of deflection measurement may be translated into another, so that empirical or established interpretation graphs can be used without the measurement having to be repeated in the prescribed manner.
In addition to the reason noted above, Whitcomb (1982) notes that the newer generation vibrating measuring devices offer significant advantages of ease and speed of operation over the
Benkelman beam and California deflectometer.
Moore et ale (1978) make the following statemen~ on the quality of such correlations: "All of the steady state dynamic deflection devices can be expected to correlate reasonably well with
static deflection measurements.
Many evaluation procedures employ these dynamic deflection devices for estimating the anticipated useful life (or loadcarrying capacity) of pavements based upon correlation of the measurements with static deflection measurements".
It is obvious though, from the discussion on deflection parameters (see 1.3.2) that the correlation of a single deflection point, like a Benkelman beam deflection, with a highly complica
ted deflection basin description will not necessarily be a good one.
For this reason Whitcomb (1982) cautions about the use of applying published correlations without some knowledge of the degree to which the two variables have been correlated.
It is more desirable to avoid the need to make the correlations at all.
The following is quoted from the FHWA study (1984) : On the correlations between NDT deflection devices "In general, a different correlation should be developed for each major pavement type and for different pavement thicknesses within particular types of pavement because the correlation is not unique,
..•.".
Regarding the interchangeability of data the following is also quoted: "The source, testing procedure and equipment configuration used in developing the data must be fully understood before data collected by another agency can be used."
(a) realistically simulate moving traffic loads in terms of magnitude of load, shape and equivalent time of loading
(b) accurately measure the whole deflection basin with high levels of reproducibility
(c) be simple to operate, so that it is possible to use it with competence in the field; but it should also be applicable to research
I. 33
(d) be capable of attaining high levels of productivity, which must reduce the cost of testing.
Considering these prerequisites, it seems that the FWD is the most appropriate of the devices discussed.
As far as cost and ease of operation in particular are concerned, the vibratory devices such as Dynaf1ect and Road Raters are also considered appropriate.
The main advantage of these newer generation deflection measuring devices lies in the fact that they normally measure at least four points on the deflection basin.
The modified RSD or Benkelman beam and a modernized Lacroix def1ectograph are able to monitor the deflection basin at frequent intervals in spite of there being only one measuring point.
The Lacroix def1ectograph is used by the road authorities in South Africa on a network basis with a proven level of efficiency.
A vast amount of information is available on various pavement structures from HVS testing and on full structural 1ives measured with the RSD and MDD on the same location.
The information gained from these devices may be used to determine suitable deflection basin parameters accurately or to perform realistic correlation studies between these parameters.
It is possible to use deflection basin measurements obtained from a modernized Lacroix def1ectograph for more detailed analysis.
To date only the maximum deflection
Us ) has been used to diso tinguish between various uniform sections of road statistically.
By the use of deflection basin paz:ameters related to specific pavement structure type and state a higher level of engineering interpretation and effective service can be provided for the purpose of pavement management, rehabilitation and overlay design.
It is suggested though, that tests be done with the FWD and vibratory deflection basin measuring devices in South Africa in view of their advantages mentioned above.
These devices will have to be correlated with the abovementioned data bank on deflection measurements from HVS sites in order to ensure uniform standards of deflection interpretation.
The parameters of the deflection basin must 
(a) re)present the full characteristics of the whole deflection basin (not only maximum deflection (0 ), but rather a combio
I. 34 nation of parameters like SCI and BCI covering the whole deflection basin);
(c) be able to relate to the structural characteristics depth of pavement structures.
of the full
From the survey it is obvious that in the past at least two deflection points on the deflection basin are normally needed in an analytical procedure.
deflection (0).
o distance relative
The other accordance with prescribed point should requirements.
preferably be varied to the centroid of the loaded area (0) r in in
Examples of such parameters are Q
One such point is the point of maximum and ST, which still require other points measured on the deflection
Another alternative basin in order to select a value of O.
r is to use fixed values of radius for deflection points, for example 00' 0305' 0610' etc.
It is suggested that the parameters that use these deflection values, for example SCI, ST, BDI, BCI, etc., be investigated in view of the guidelines described above and the equipment available in South
Africa.
A further suggestion, which will be discussed in more detail in· a later section, is that these selected parameters be related to the pavement structure classification
(NITRR, 1985a) and to pavement performance models.
used in TRH4
A parameter like SCI will then be determined differently for a granular base than, for example, from for a cemented base pavement, reflecting its different deflection basin characteristics formance.
and structural per
MEASUREMENT AND DATA PROSESSING OF
DEFLECTION BASINS IN SOUTH AFRICA
2.1
Measuring equipment
2.2
The procedure
2.2.1
Site selection and preparation
2.2.2
Measuring procedure
3.1
Preautomation data evaluation (Rebound procedure)
3.2
Automated data evaluation (WASHO procedure)
4.
THE NEED FOR CURVE FITTING PROCEDURES
5.
PROPOSED DEFLECTION BASIN MEASURING EVALUATION PROCEDURE
5.1
Data manipulation and preparation
5.2
Higher level deflection basin data manipulation
6.
CONCLUSIONS AND RECOMMENDATIONS
2.9
2.14
2.
1
7
2.19
2.19
2.20
2.25
2.2
2.2
2.2
2.3
2.3
2.6
In South Africa the use of the full deflection basin was generally neglected in the analysis of deflection basin parameters.
In the past the analyses were mostly concentrated on the small area of the deflection basin in the vicinity of maximum deflection.
In the program of accelerated testing with the Heavy Vehicle Simulator
(HVS) fleet in South Africa. the whole deflection basin is measured on the surface and in depth of the pavements.
The same limitation of data analysis was concentrated on the small area of the deflection basin near the vicinity of the maximum deflection for these depth deflection basins measured.
In this chapter a brief description is given of how the surface deflection basin is measured in South Africa by means of the automated Benkelman beam or also called the road surface deflectometer (RSD).
The procedure and equipment to measure the deflection basin at various levels in the depth of a pavement by means of a multidepth deflectometer (MDD) are also briefly discussed.
The present data analysis procedure is discussed.
Based on this and a discussion of the whole deflection basin and related parameters.
the author suggests changes to this data analysis procedure.
Specific reference is made of the need for a better description of the full deflection basin • Curve fitting models are discussed briefly and recommendations are made for practical use with the road surface deflectometer (RSD) and the deflectograph •.
HVS testing is done by repeated application of a chosen wheel load to the road structure.
Several sophisticated instruments are used
to monitor the response of the road.
In the field. a microprocessor system is used to record the measured data on a magnetic disc.
The data on the magnetic disc is then transported to the central laboratory in Pretoria for processing by the main computers (Freeme. et al .• 1981).
During an HVS test the measurements of the surface deflection and curvature of the pavement with an automated Benkelman Beam.
also called the Road Surface
Deflectometer (RSD) (Basson.
1985).
are collected as data.
Elastic deflection and permanent deformation measurements are taken at different depths within the pavement using the multidepth deflectometer (MOD).
(Basson. et al. 1980.)
The MOD is a device that can simultaneously measure the vertical deflections and permanent deformations of up to six points on a vertical line in any pavement.
The methods of site preparation and illustration of the MOD is shown in Figure 2.1.
The RSD is an electronically instrumented deflection beam which can measure dynamic resilient deformations to an accuracy of
±
0.01
mm.
(Shackel. 1980.) This modified Benkelman Beam ( the RSD) and the use of the RSD and MOD plus other related instruments are illustrated in Figure 2.2.
The modules of the MOD and the measuring point of the RSD make use of a linear variable differential transformer (LVDT) to measure pavement deflections.
This discussion serves only as a brief description of the equipment used to measure deflections in depth and on the surface of a pavement structure being tested with the HVS.
A typical HVS test section is selected after a deflectograph survey of the road length was done.
Uniform sections of the road are then identified which differ significantly statistically.
A decision is made whether to select a section that represents for example the 85th percentile.
15th percentile or average of the road in terms of the deflectograph survey.
A detail survey of each meter of normally a 100 meter section is
SURFACE COVER
SURFACE CAP
SURFACE COVER
SEAL
SOCKET CONNECTOR
SURFACE CAP
MOO MODULE
LVOT CORE
RUBBER. LINING
RUBBER SLEEVING
INTER CONNECTING ROO
FIGURE 2.1
METHODS OF SITE
PREPARATION OF THE
MULTIDEPTH  DEFL ECTOMETER
HVS.TEST
WHEEL
MULTI DEPTH
DEFLECTOMETER
~
WHEEL SPEED/POSITION
WHEEL LOAD
C
PERMANENT AND ELASTIC DEFLECTION
TEMPERATURE GRADIENT
•. SOIL SUCTION PROFILE
ELASTIC DEFLECTION
LVDT
FIGURE 2.2
THE HVS SECTION INSTRUMENTATION
then carried out with the standard Benkelman Beam.
Based on these results a 8 meter section of road is selected which is uniform in terms of its maximum deflection measurements.
Other factors such as road safety, gradient etc. are also considered in the selection of such an HVS test section.
(Shackel, 1980.) In some cases, particularly short experimental sections, the selection of a site may follow a different procedure, but the aim is normally to have at least an
HVS test section that is uniform over its 8 meter length in terms of Benkelman Beam deflections.
The instrumentation and marking of such a selected test section is as shown in Figure 2.3.
As can be seen, normally at least two MOD holes are installed while the RSD measuring points are marked on the surface in order to represent the whole section and enhance repeatability.
The dual wheel with the specified tyre pressure and load is moved
±
3 meters away from the measuring point.
The deflection produced by the load approaching the measuring point of either the RSD or MOD is recorded on a chart as a continuous trace, while switches, at measured distances along the road, record the passage of the load passing them.
A typical trace is shown in
Figure 2.4.
The square waves of the switches reflect the variance in speed at which the wheel load approaches the measuring point in order to facilitate the correction to relate distance to deflection accurately.
The loaded wheel moves past the measuring point for a distance of about 1,2 meter whereafter pulses simulating measurements are generated automatically to complete the standard set of 256 measurements of a deflection basin. Each measured point on this set is a standard distance apart, usually 22,07 mm, depending on the switch characteristics.
Usually measurement sets with the MOD are taken only on the centre line and with the RSD in line with the measurement point.
Offcentre measurements can be taken with the MOD.
At
M
=
MUL T1 DEPTH OEFLECTOME~TER o =
ROAD SURFACE OEFLECTOMETER
P
C
=
PROFILOM£TER
=
HOLE FOR NUCLEAR MOISTURE METER
PRETOR1A~
E£:
CROSSFALL
~~.5m~1
2
3
0
P
4
200 mm
M
°T
ol
200 mm
0
5 6
P
7
P
8m
8
0
M
D
P
..
KRUGERSOORP
9
TEST SECTION 136A4 WATER HOLES
200mm FROM SECTION EDGE EACH O,6m DEEP
;1~ ~I t
1m
0
0
M
0
14
~
WATER TABLE HOLES
15 16
10
II 12 13
P P
FIGURE 2.3
TYPICA L LAYOUT OF TEST AND CONTROL SECTION
.
N
....,
FIGURE 2.4
TYPICAL RECORDED CHART FROM RSD MEASUREMENT SHOWING DEFLECTION AND SQUARE
WAVE PRODUCED
least 2 measurement sets are taken as control at each measuring point of the RSD and MOD at a speciffic time during the testing.
Various wheel load and tyre pressure combinations are used during measurements.
It is important to note that the method of measurement of the standard Benkelman Beam and that of the RSD and MOD under HVS condi tions differ.
The RSD and MOD measurements use the WASHO procedure (Monismith, 1979) while with the standard Benkelman
Beam the rebound procedure is used.
In the WASHO procedure the load approaches the end of the probe or measuring point and the deflection is observed.
In the rebound procedure the wheel moves away from the measuring point and rebound of the pavement is measured.
Rebound deflection is about two times the deflection measured with the WASHO procedure.
This may vary with the type of pavement measured.
This is probably due to plastic deformation.
The Benkelman Beam was used very effectively by Dehlen (1961) to measure deflectiondistance curves manually.
This was done by measuring the deflection basin manually at 3 inch (75 rom) intervals as the wheel load approached the measuring point.
Smooth curves were drawn through the plotted points.
Particular care was taken over the central 2 feet (610 rom), and any irregular curve rejected.
This is illustrated in Figure 2.5.
The maximum deflection was obtained directly from the observations.
The radius of curvature at the point of maximum deflection was obtained by determining the circle which is the best fit to the curve over the central 6 or 9 inches (150 to 225 rom).
The radius of curvature of the road surface was then computed from the radius of the circle of best fit from the formula;
R
= v r.h2
Radius of curvature measured
<Feet)
150
FIGURE 2.5
EXAMPLE OF THE PLOTTING OF DEFLECTION OBSERVATIONS
AND MEASUREMENT OF RADIUS OF CURVATURE
where R = radius of curvature of road surface, v r • radius of plotted circle, in the same units as R,
= vertical scale of plot expressed as a dimensionless ratio, h • horizontal scale of plot expressed as a dimensionless ratio
Dehlen (1961) noted that a circle fitting the deflected surface in the field became an ellipse when plotted to different horizontal and vertical scales.
Thus ideally, determination of radius of curvature from the deflection plot should be made by fitting ellipses.
Dehlen (1961) estimated that the error introduced by fitting circles however, was not likely to exceed 5 per cent.
It is also observed by Dehlen (1961) that care and experience is necessary for the accurate determination of the radius of curvature from the observations.
The Dehlen curvature meter developed by Dehlen (1962a), enabled measurement of the curvature directly, as illustrated in
Figure 2.6.
The relation between curvature and differential deflection may be deduced by simple geometry by fitting an appropriate curve to the three points on the road surface defined by the instrument.
Dehlen (1962a) indicated that using a parabola, the radius of curvature is given by
L2
R· 
26 where 6 is the differential deflection
L is the distance between the deflection gauge and each support
Dehlen (1962b) observed that a study of numerous deflection patterns obtained over a period of time indicated that in the vicinity of the points of maximum deflection the curves are typically of a sine form.
It has also been noted that points of inflection
(points P in Figure 2.7, where the curve changes from concave to convex) occur fairly consistently at distances (5) of 6 inches
(150 mm) on either side of the point of maximum deflection.
The
DEFLECTION MEASURING
INSTRUMENT
0
RADIUS OF CURVATURE
R
DEFLECTED SHAPE
OF ROAD SURFACE
FIGURE 2.6
DIAGRAMMATIC SKETCH SHOWING THE PRINCIPLE OF
THE CURVATURE METER
MAXIMUM
TOTAL
DEFLECTION
*
FIGURE 2.7
TYPICAL PATTERN OF DEFLECTION OF A ROAD SURFACE
BENEATH A LOADED WHEEL
relation between radius of curvature (R) and differential deflection (6) in the case of a sine curve is
With F
R = 7
6
=
2.3 and L
=
5 inches (127 mm) the formula is reduced to:
A program BENKI was written by Szendrei (1974) and later updated as BENK5 (Szendrei.
1975(a» to evaluate the automated Benkelman
Beam (RSD) field data on computer.
These programs were later updated again by (Szendrei.
1975(b» to accommodate the processing of the MOD deflection data too.
In these programmes the deflection tracer.
as supplied from the field measurements.
is defined by 11 points of the original 256 points measured.
along the length of the trace.
The points on the chart are converted to true road distances and road deflections.
The result of these operations is to produce 11 points on a plot of road deflections versus road distances.
The 11 points lie on a plot as shown in Figure 2.8 which still follow the basic shape.
although somewhat distorted.
Szendrei (1975(a» noted that the top part of the curve down to some level PQ (Figure 2.8).
which is about 30 per cent of the maximum.
approaches a probability represented by the equation; curve closely.
This is y x
=
A exp (kx
2) in which A is the maximum amplitude occurring at
=
0 and k is an attenuation constant which determines the width of the curve.
Below PQ.
(see Figure 2.8) a linear interpolation method was followed.
The values of k and A are determined by
)Ii x x
OBSERVED POINTS x
FITTED CURVE (ABOVE PO) x INTERPOLATION (BELOW PO) z
....
U lLJ
oJ lL.
lLJ a a
«
0
0:::
U) z
0
0:::
U
~
A
P
\
o
\
\
\
\
\
"
.....•••..
'
FIGURE 2.8
FITTING OF EXPONENTAL CURVE TO MEASURED POINTS OF THE POSITIVE
using the y coordinates of the measuring points from point 2 down to level PQ.
The standard estimated from; error e of the fitted curve can then be e:ll
./r.d~/n
~ in which d.
~
"" deviation of observed point from value calculated from the fitted curve (y.
A exp (kx~» and
1.
~ r.
indicates the summation for all n points observed above level PQ.
The main aim of these programs are to determine the radius of curvature at the point of maximum deflection.
By using the general formula of radius of curvature (Szendrei.
1975(a» at any point along a curve defined by y
= f(x).
radius of curvature is given by;
I
3/2
For the curve fitted.
Szendrei (l975(a» curvature at any point along the curve: derives a radius of
(l
+
4k
2 x
2 y
2
2ky (2kx
2
1)
)3/2
The minimum radius of curvature.
occurs at the point of maximum deflection x = of the curve.
Substituting the values of y = A and a into this derived equation.
Szendrei (1975(a» derives;
R "" 0.5
kA
Using Dehlen
I s radius of curvature formula, R "" measured in nun and L
7
6' when 0 is
=
127 nun.
Szendrei (1975(a» made a more direct comparison with the Dehlen radius of curvature.
This is done by calculating deflection 0127 at 127 nun from the deflection basin.
Assuming that the curve is sYmmetrical about the vertical and passing through the maximum, the values of 6
127 will
be the same on both sides.
Differential deflection 6, as described by Dehlen and corresponding to the measurement of the
Dehlen curvature meter instrument is then expressed as follows:
To find the mean radius of curvature between x
127 rom, where x
=
127 rom and x
=
=
0 at the maximum of the curve, a solution for the circle with origin at (o,y ) and intersecting the exponential o curve (Zendrei, 1975(a) at x
=
+ 127 rom is closely approximated by;
8.065
6
Szendrei (1975(a» noted that this formula gave a discrepancy of
14 per cent if compared to the Dehlen radius of curvature.
This does not necessary reflect the difference in the model used to fit this part of the deflection basin.
It must be remembered that the difference in measuring procedure (WASHO versus rebound), for the particular pavement type compared, will also contribute to this difference.
In the preceding sections it was illustrated that even with the automated Benkelman Beam or RSD, the emphasis was to measure mainly two deflection basin parameters, namely: maximum deflection (6 ) o and radius of curvature (R).
Both these parameters are measured in the area of positive curvature of the deflection basin (see Figure
1.7).
This is only a very small part of the whole deflection basin.
The fact that these two parameters alone are reflecting only limited information available from any possible deflection basin of any particular pavement is described in full elsewhere.
(Horak, 1984.)
In the development of fundamental methods of pavement evaluation by means of deflection basin measurements it is imperative that an
accurate description of the deflection basin is obtained.
In Table
1.1 a summary of deflection basin parameters and their respective formula are given (Horak, 1984).
The level of description of the deflection basin varies from a singular point to a highly sophisticated polynomial function.
It is clear though that there is a move towards incorporating parameters of the deflection basin that attempt to describe the reverse curvature (see Figure 2.7) of the deflection basin too.
Horak (1984) clearly indicates that there is reason to believe that deflections measured (and their related parameters) on the outer edges of the reverse curvature of the deflection basin give a clearer indication of the structural value of the subgrade.
Deflections measured nearer to the point of maximum deflection (on the positive curvature, Figure 2.7) give a better indication of the structural value of the upper layers.
The structural effect of the lower layers are also reflected by these parameters and the need arises therefore to separate these effects by g1v1ng more attention to the proper description and measurement of the reverse curvature of the deflection basin.
The preceding sections indicated that the standard procedure at any
HVS test section is in fact to measure the whole deflection basin very accurately with the RSD on the pavement surface and the MOD in depth of the pavement.
As stated earlier the data evaluation of these curves were traditionally only focused on the related parameters of the positive curvature part.
In fact the model for curve fitting used, only attempts to describe the 30 per cent part of maximum deflection while the reverse curvature part is linearly interpolated.
Only 7 selected points on the positive curvature are used to do curve fitting with (see Figure 2.8) in the Szendrei model
(1975(a».
This can lead to a misrepresentation statistically acceptable fit is achieved.
although a
There exists a discrepancy in the interpretation of or calculation of radius of curvature (R) if the Dehlen radius of curvature and the
Szendrei radius of curvature is calculated.
The Dehlen radius of curvature measurement uses, the rebound method while the Szendrei radius of curvature, from RSD data.
is measured with the WASHO procedure.
The maximum deflection differs by a factor of two when these two procedures are compared.
It is obvious that the radii of curvature will also be influenced.
While the circle being fit through points at ±127 mm and maximum deflection (through 6
0) in the
Dehlen procedure of radius of curvature calculation, the Szendrei procedure only require it to intersect at ±127 mm on the deflection basin.
Both radii of curvature further do not really comply to the strict definition of radius of curvature as two or three points are intersected.
Curvature at a point is the rate at which the curve is turning away from the tangent line at that point and radius of curvature is the reciprocal of curvature.
(Bedford et al., 1970)
For such calculations, a proper definition of the curve is needed mathematically.
Factors such as plastic deformation and reverse curves within the positive curvature centre (Horak, 1984) can remove radius of curvature calculations even further away from a soundly based scientific definition and interpretation.
The standard evaluation of maximum deflection and Dehlen radius of curvature of the RSD and MOD results lacks the freedom or ability to do more sophisticated analysis of the pavement structurally.
The need arises therefore to relate deflection basin parameters of the whole deflection basin to specific structural layers or zones or behaviour states.
The vast amount of RSD and MOD measurements available from all the
HVS tests and quality of measurements make it imperative that better use of the whole deflection basin measurements must be made.
New models and procedures should be investigated to evaluate such deflection basin data.
In Section 3.2 it was described how RSD and MDD deflection basin data are prepared.
At the stage before the modelling of the positive curvature (see Figure 2.7) is done, the data is in a standard form where the 256 measurements of deflection are correlated correctly to horizontal distance.
In Figure 2.9
a graphical illustration is given of such a typical set of measurements.
As can be seen the deflection has, as measured, a negative sign and the origin is not at the point of maximum deflection (6).
The possibility of the reference points of the o
RSD being inside the deflection basin and leading to incorrect deflection measurements increase significantly as the loaded wheel passed the measuring point (point of maximum deflection).
Additionally there exists the danger of plastic deformation at particularly higher wheel loads, interfering with the quality of deflection measurements, as the wheel passes the measuring point and slowing down to a halt.
For that reason the author decided to work only with the first part of the curve up to the point of maximum deflection.
In order to make calculations easier too, the negative sign of the deflection was reversed and .the origin was chosen at the point of maximum deflection.
The description of the programmes and procedures to do these manipulations on computer are given in detail by Horak and Otte (1985).
In some cases
"spikes" occur due to interferences like wind, touching wheels, etc., on the original data set (as in Figure 2.9).
This is first smoothed out by a standard programme procedure (Horak and Otte,
1985).
The final data set, as prepared, is then stored on computer in a format whereby the deflection and horizontal distances are correctly related.
A graphical presentation of such a data set is as shown in Figure 2.10.
Such a data set of a deflection basin measurement can now be defined as edited for further data manulipulation. As will be seen in the next section such data manipulations can be done with various levels of sophistication.
The form in which a data set of a measured deflection basin is, as described in the preceeding section, ideal to calculate all the
KEY:
DATE MP
810721 6
REPETITIONS
564235/LOADS
0,55
0,0
22,5 30,0 37,5
DISTANCE (mm x 10
2)
FIGURE 2.9
TYPICAL RSO RESULTS OF
. DEFLECTION BASIN MEASUREMENTS
0,30 i= u

E
E
z
0
0,25 lL.
LLI
0
0,20 o
7,5 15 22,5
DISTANCE (mm x 10
2)
30
FIGURE 2.10
TYPICAL MANIPULATED R SO DEFLECTION BASIN HALF
OF DATA SET
deflection basin parameters as discussed in Chapter 1.
The various deflection basin parameters and their respective formula as found in the literature survey are all shown in Table 1.1.
In
Table 2.1
the number of deflection basin parameters has been reduced to 11. All these deflection basin parameters listed here can be calculated by using deflection points at standard offsets on a specific deflection basin data set. These deflection points are at the offsets of 0, 127, 305, 610 and 915mm.
These deflection points can easily be determined by a simple interpolation procedure ( Horak and Otte, 1985) on such a prepared data set.
This expands the description of the deflection basin considerable if compared to the traditional limited description of the deflection basin by calculating only the first two parameters listed in Table 2.1 ( maximum deflection and radius of curvature).
The author also explored the area of a mathematical expression for the whole deflection basin.
The measured deflection basins are discrete points and various mathematical and physical models available were selected and tested to fit these discrete measuring points.
The SPSS Statistical Package for the Social
Sciences (Nie et aI, 1975; Robinson, 1984) was used to do linear and nonlinear regression analyses.
This work is described in detail in Appendix A. When linear regression analysis procedures are used mathematical models can either describe the area of positive curvature or that of the negative curvature well, but not both areas simultaneously (see figure 2.7).
This regression analysis method also cause a slight distortion in the area of positive curvature.
The use of the nonlinear regression analysis procedurea does lead to improved fittings of either the positive or negative curvature of the deflection basin (see figure 2.7).
The mathematical models still either describe the positive or negative curvature well, but not both.
The physical model of a point load on an unlimited beam on elastic foundations gave the best fit using the nonlinear regression analysis procedure.
It also gave a better fit of the whole
Parameter
I. Maximum def lection
2. Radius of curvature
3. Spreadability
4. Area
5. Shape factors
80
Formula
Measuring device
Benkelman beam
Lacroix deflectograph
Curvaturem eter
Rr
2
2 80
(8018
r  I ) r
=
127 mm
S
[(80
+
8
1 +
8
2+83)/5]
100
Dynaflect
80
8
1
""8
3 spaced 305mm
A
:I
6
[I.•.
(8
1
/8
0)
+
2*
(~/80)
+
8
3
/8
0]
Falling weight deflectometer(FWD)
F
1
=
( 8
0 
8
2)
I
8
1
F
2 •• ( 8
1 
8
3)
I
8
2
SeI
=
80 8r ) where r
 305
mm or r
 500
mm
8 CI
=
8
610
8
915
FWD
Benkelman beam
Road rater
FWD
Road rater
6. Surface c u rva ture index
7. 8ase curvature index
8. Base damage index
9. Deflection ra tio
10.Bending
index
II. Slope of deflection
801
=
8
305 
8
610
Road rater
Qr = 8r
180
where
8r ~
80/2
81 
8
la
where a
II
Deflection basin
SO
:I ta n•
I
(8 0  8 r)
I
r where r
:I
610 mm
FWD
Benkelman beam
8enkelman beam
deflection basin, but still lacked accuracy in the small area of maximum deflection (see figure 2.7 or Appendix a for detail).
The combined use of a mathematical model in this area solves the problem.
The use of the physical model leaves the opportunity for detailed evaluation on a theoretical basis. This aproach was not pursued further in veiw of the fact that various deflection basin parameters
, as described above, can be calculated with ease with a high degree of description of the full deflection basin. The practical and simple approach was therefore selected by this author to be pursued in this thesis rather than such a highly theoretical approach in spite of the challenging possibilities.
(a) The measuring equipment, RSD and MOD, associated with the accelerated testing of the HVS is highly sophisticated and accurately measure deflection basins on the surface and in depth of pavement structures.
statistically representative
The measuring procedure ensures deflections of a pavement structure.
(b) The evaluation procedures of typical Benkelman beam and Dehlen radius of curvature meter measurements are not automated and limited deflection basin information in the vicinity of maximum deflection is gathered and processed.
The data evaluation procedures of these rebound measurements are peculiar to the method and equipment.
(c) The measuring procedures of the RSD and MOD are automated and the whole deflection basin is recorded.
The evaluation or data processing procedure make use of model curve fitting, but interest is concentrated on the small area of positive curvatu~e while the large negative curvature of the basin is virtually ignored.
The WASHO procedure of measurement is relatively free of plastic deformation effects and is preferred to the rebound method.
(d) For fundamental methods of pavement evaluation it is imperative that an accurate description of the deflection basin is obtained.
Various deflection basin parameters can be used to reflect the whole defl~ction basin and associated structural relationships.
(e) Only the elastic side of a typical
RSD or
MOD deflection basin is processed to ensure that the data is relatively free of plastic deformation and possible interferences of reference points in the deflection basin.
(f) The data preparation procedure.
even before model curve fitting is done.
can provide as measured deflections (60, 6127• 6305,
6610• 6915 and 62000) which is normally used in the calculation of the majority of deflection basin parameters.
It is suggested that this approach should be followed for normal data processing.
(g) Higher level data manipulation using linear and nonlinear curvefitting procedures were used to express the discrete set of measuring points of a deflection basin mathematically.
The most successfull model was that of a point load on an elastic foundation using nonlinear regression analysis techniques. This shows great promise .but is not persued further here due to the obvious ease and accuracy of the simpler approach mentioned above.
ANALYSIS or
DEFLECTION BASINS MEASURED
DURING ACCELERATED TESTING
2
2.1
2.1.1
2.1. 2
2.1.3
2.1.4
Behaviour of deflection basin parameters with repetitions
Bitumen base pavement
Granular base pavement
Cemented base pavement (equivalent
Light structured granular pavement
3.3
3.3
3.3
3.7
3.10
3.14
In the preceding chapters it was described how the deflection basin can be described by means of various deflection basin parameters.
The use of these parameters with the road surface deflectometer (
RSD) was proposed as a viable analysis technique as the RSD accurately measures the full deflection basin. It was also shown how the analysis of the measured RSD deflection basins can be simplified to calculate all the deflection basin parameters as shown in Table
1.1.
Up to date,the RSD is associated only with the accelerated testing facility ,the fleet of heavy vehicle simulators (HVS's).
As a vast number of pavement sections have been tested over the years, there exists potentially a vast data bank of information on RSD measured deflection basins.
The original data processing of the accellerated tests were however done with other goals in mind. The result is that this RSD data is stored on magnetic tape in an ackward format.
Detail background information of specific tests is further needed to aquire the neccessary information in the raw data form.
Due to this cumbersome process of getting the data it was therefore decided to concentrate the effort on tests on typical representative pavement types tested where there is a high confidence in the knowledge of the detail of the test information.
These tests selected would then act as a pointer for possible detailed analyses as a seperate project.
Accelerated tests carried out with the Heavy Vehicle Simulator (HVS) fleet on four different pavement structures were selected for a detailed analysis of the deflection basin data measured.
The four
HVS tests selected are representing pavements with a bituminous base on a cemented subbase (Opperman et al., 1983), a typical granular base on a cemented subbase (Horak and Maree, 1982), a typical light granular pavement structure (granular base and subbase) (de Beer
1982 and Van Zyl and Triebe1, 1982) and a cemented base and subbase
(Opperman, 1984 and K1eyn et al., 1985).
The latter three have thin asphalt surfacings (~ 40 mm) which is typical of South African roads.
The test on the cemented base pavement has particular significance too: it is the only HVS test where, after the
completion of the initial test, the test section was overlaid and the test was continued on the overlaid section.
The curve fitting procedure described elsewhere (Horak, 1985 and
Horak and Otte.
1985) was used by this author to calculate the deflection basin parameters from the deflection basins as measured during the HVS tests. Due to the small sample size of the relevant data sets the discussion on the relationships between the structural parameters of each individual layer and the calculated deflection basin parameters mean that no meaningfull regression analyses could be done.
The discussion on this is therefore more general and directed towards the graphical evidence presented.
The behaviour of the various deflection basin parameters related to the behaviour of the various pavement types under accelerated testing is discussed in detail.
Suggestions are made as to the usefulness of these deflection basin parameters to describe pavement behaviour states and layers.
The fold out at the back (Table 1.1) referring to the various deflection basin parameters should be used for ease of reference.
The various parameters, as calculated under a 40 kN dual wheel load, were related to the actual number of repetitions of the
HVS test at Paradise Valley (Opperman et al., 1983).
Parameters were grouped together in terms of units and range and all presented versus actual repetitions as shown in Figure 3.1.
Although the actual test consisted of 2,3 x 106 actual repetitions, only about 1,5 x 106 actual repetitions are shown in Figure 3.1.
In general, deflections (60 to 6915) show a tendency to increase slightly with number of actual repetitions.
This is as expected.
What is significant though is that 6305 and 6610 show
z o ot;
Ou.
..Jw
(1')0
50
<l: w
Q::
<l: o
W
1
<l:(\l ll:
E w
I
Z
AO 3000
/
AO127.
AI27305.
A305610
' I
/1
A 610915


F2
Q
F1

V

5 ll:
Q.
(I')
(I')

>j~
40
m;
<l:w o ll:
20
~<l:
0
A
~~E
0,03
1
~~!
~~~==~==
=============
0·· 
~:8Dcs.IICIj
z o f= 
0,1 u
E w
E
..Ju.
W o 10
1
8127
8
305
8610
8915
10
3
10
4
ACTUAL REPETITIONS
FIGURE 3.1
DEFLECTION BASIN PARAMETERS VERSUS ACTUAL REPETITIONS
FOR A BlrUMEN BASE PAVEMENT
some relative increase in deflection to 6915, which is virtually constant.
This may reflect a change in elastic moduli of the subbase and selected layer (Tam, 1985).
In the region of 105 to
106 actual repetitions all deflections (60 to 6915) level off.
If these results are compared to the change in calculated effective elastic moduli as shown in Figure 3.2, it is confirmed that the subbase, selected layer and subgrade show the greatest change in this region (105 to 106 actual repetitions).
The index parameters, surface curvature index (SCI), base damage index (BDI) and base curvature index (BCI) also reflect the same changes as their calculations are based on the values of 60,
6305, 6610 and 6915, SCI shows only a slight increase in value wi th increase in actual repetitions.
This reflects a bitumen base which is structurally strong, with minimal change in effective elastic moduli deeper in the pavement structure
(Kilareski et al., 1982).
This corresponds with the change in effective elastic moduli as shown in Figure 3.2 for the s~bbase, selected layer and subgrade over the range where their elastic moduli showed the greatest change.
The slightness of change in
BDI and BCI are indicative of the scale of change of the effective elastic modulus of the cemented subbase which still had a high residual effective elastic modulus at the end of the test.
Parameters such as spreadability (S) and area (A) reflect the whole of the deflection basin.
The major portion of the deflection basin, particularly away from the point of maximum deflection, reflects changes in the lower layers (Tam, 1985) .
Figure 3.2
indicates that the changes in effective elastic layers were relatively small.
This may contribute to S and A being relatively constant.
Shape factors (Fl and F2) and deflection ratio (Q) are not specifically related to any structural layers.
In the calculation of these parameters the shape of the deflection bowl, or change thereof (e.g. becoming more peaked), would be reflected.
This apparently did not happen.
~
~ 2000
(/) t
(/)
« w lL.
o
·1500
> to
W lL.
(/)
::>
1
::> a o
~ w
1000 lL.
W
500
SUBGRADE (IN SITU MATERIAL)
SELECTED LAYER (DECOMPOSED SANDSTONE)
1.0
REPETITIONS (MILLIONS)
1.5
FIGURE 3.2
CHANGE IN EFFECTIVE EMODULI OF THE DIFFERENT LAYERS IN THE HVS TEST /62A3
AT PARADISE VALLEY (OPPERMAN ef 01.,
/983)
The statement above is enhanced when the fitted deflection basin functions (Horak, 1985) are integrated over various segments
(e.g. 0 to 127 mm, etc.).
Virtually no changes took place until about 1 x 106 actual repetitions.
AO3000, which is the integrated area under the whole deflection basin, shows very clearly only a slight change after 1 x 106 actual repetitions.
Slope of deflection (SD) shows a gradual rise in value as actual repetitions increase.
This parameter can unfortunately not be related to any change of any particular structural layer.
It is however an indication of a deflection basin which is becoming gradually more peaked, but can, due to the low range it is covering, not be defined as peakea.
The various parameters, as calculated from deflection basin measurements under a 40 kN wheel load, are presented for the HVS test at Erasmia (Horak and Maree, 1982) in Figure 3.3.
The deflection basin showed definite changes with the increase in actual repetitions.
Although 6915 showed virtually no change,
6610 and 6305 to 60 in particular showed the greatest changes.
This clearly indicates changes in the base and subbase effective elastic moduli (Tam, 1985).
In Figure 3.4
it can be shown that the base and the subbase in particular did change considerably in terms of effective elastic moduli up to around 2 x 105 actual repetitions.
This change in the base and subbase effective elastic moduli is clearly reflected by the change in surface curvature index (SCI)
(Anderson, 1977).
The base damage index (BDI) and base curvature index (BCI) changed to a lesser extent, indicating changes in the effective elastic moduli of the selected layer and the subgrade (Kilareski and Anan, 1982).
Radius of curvature (R) showed a definite reduction as actual repetitions increased which confirms the indication of the SCI values.
Spreadibility (5) and area (A) did however not reflect any
600
0
!!!
z 400
01
0 llJllJ
0...1
011..
..JllJ
(/)0
200
0
SO


ON llJE
~.s
a::<t
200
100
~llJ
Ia:: z<t
0
2
AO3000
I
I
AO127. AI27305.
I
I
I
I
I
A305610
I
I
A 610915
~_:=_
:=_:=_:=_:=_'"::_
~=:_~=:_~=:_===_"':
=_:=_ :=_
:=_ :=_
:r"
+
:2 t==_1
0
0
Z
(/) a:: llJ
IllJ
:E
<ta::e
~.s
x llJ
0,3
0,2
0,1
0
0,5
SCT

BOI
BCJ: z
0
I
0 llJ
..I
II..
llJ
0
0,4
E

E
0,3
0,2
0,1
0
10
1
ACTUAL
10
3
REPETITIONS
10
4
8
915
82000+830 0
10
5
FIGURE 3.3
DEFLECTION BASIN PARAMETERS VERSUSACTUAL
REPETITIONS FOR A TYPICAL GRANULAR BASE
PAVEMENT

1200
~ 1100
::E 1000
II)
3
900 g
800 o
::E 100 u i=
600
II)
500
W w
400
> 300
I
~ 200 u.
u.
100
w
ROAD P391 I; TEST 136A4
• E BASE
X
E SUBBASE
4
E SELECT o
E  SUBGRADE
7 0 kN ••.
t,l~
100kN
WHEEL LOAD WHEEL LOAD r
WATER
INDUCED
300 400 500 600 700 800
NUMBER OF REPETITIONS (
X
10
3)
900 I 000 1100 1200 1300
FIGURE 3.4
AVERAGE EFFECTIVE
.
DUAL WHE£LLOAD (Horak and Moree, 198 )
change.
Their values were slightly higher than those of the bitumen pavement but were also constant.
The parameters.
shape factors (Fl and F2) were the same and showed a steady increase in value with the increase in actual repetitions.
This is generally the same as the behaviour for bitumen base pavements.
indicating a more peaked deflection basin developing.
Deflection ratio (Q) stayed rather constant.
reflecting no particular change of any structural layer.
The integrated area under sections of the function of the fitted deflection basin showed a slight increase in values for all the sections.
The slope of deflection (SO) indicated by its change that the deflection basin is becoming more peaked.
The initial value was higher than that of the bitumen base pavement.
which clearly indicates that this granular base pavement had a much more peaked deflection basin from the start.
This clearly reflects the lower effective elastic moduli of the granular base too.
The deflection basin parameters were determined for the cemented base pavement at Hornsnek (test 214A4) which was in a flexible state. exhibiting eqUivalent granular behaviour from the start of the test (see Figure 3.5).
This is a rehabilitated or overlaid pavement (Opperman.
1984).
In Figure 3.6
the deflection basin parameters are shown in relationship to the actual repetitions.
The deflections generally increase as measured at various points on the deflection basin (00 to 0915)' The deflection furthest out (° 915) showed only a slight increase with the increase in actual repetitions.
It is however 0610 and 0305 which showed the greatest increase. reflecting changes in effective elastic moduli of the deeper layers (Tam.
1985).
The 0127 value actually showed less increase than the 0305 value.
This is typical behaviour of a granular base. as described earlier with a cemented subbase.
Opperman (1984) reported that due to the
z
248
I
<l:
~ a: o
w
o
32
HVS RESULT
BEFORE ASPHALT
SURFACING
HVS RESULT AFTER ASPHALT
SURFACING (40 mm
THICK)
APPLIED TO SECTION
0,3 0,6 0,9
NUMBER OF REPETITIONS (MILLION)
E
E z24 o
I
<l:
~ a: o
~ 16 o
HVS RESULT
A FTER BITUMEN
RUBBER SEAL
APPLIED TO SECTION
WATER
100/N
CRACKS APPEARED IN
BITUMEN RUBBER SEAL t
x~xx~
/'
0,10 0,2
NUMBER OF REPETITIONS (MILLION)
FIGURE
3.5
AVERAGE DEFORMATION OF THE ROAD SURFACE AFTER
REHABILITATION MEASURES (ROAD 30 HORNSNEK)
(OPPERMAN, 1984)
(Jl
0:
0
~
U_
<l: N lJ.lJ.
~+
<l: z~
(Jl_
4
2
0
e§
100
~~
0:_
lJ.w::!
00: III
;:)<l:~
(Jl~
0
<l:
50
~~<l:;
00:
Ww
&:
0:
O:U(Jl<l:
0
(Jl
0:
w
~
0

0,4
0,3
~ z
<l:~2
0,2
O:e~
~eu
w
x
..J
w
lJ.
0
W
0,1
~
0 0
0,8
R
S
A
SCI
0
Bor
BCI z
0
~
U e e
0,6
0,4 lJ.
w
0
0,2


=:::::::

8
0
8
127
15
30s
8
610
8
916
10
3
10
4
.ACTUAL
REPETITIONS
FIGURE 3.6
DEFLECTION BASIN PARAMETERS VERSUS ACTUAL
REPETITIONS FOR A TYPICAL CEMENTED BASE
EXHIBITING EQUIVALENT GRANULAR BEHAVIOUR
~
crushing of the upper cemented base and limited cracking of the cemented subbase layer under the soft interlayer this is exactly the case.
The index parameters (5CI, BDI and BCI) confirm the observation of the change in the lower layers (subbase selected layer and subgrade) while the base is rather stable.
The surface curvature index (5CI) stayed virtually constant with the increase in actual repetitions.
The initial value is however in the same order where the granular base pavement, discussed earlier, ended.
The base damage index (BDI) and base curvature index (BCI) showed a steady increase with the increase in actual repetitions.
These values also started off at the level where the typical granular base pavement, discussed ear Her.
ended.
This definitely confirm the changes in effective elastic moduli of the cemented subbase, selected layer and subgrade.
The deflection ratio (Q) shown with the index parameters in Figure
3.6
is virtually constant up to 105 actual repetitions whereafter it declines.
Unfortunately it does not indicate any specific relevance to structural change in the various layers.
The parameters, spreadibility (5) and area (A), like in the case of the granular base and bitumen base pavement, are constant and more or less in the same range.
This again leads to the conclusion that these parameters are not sensitive to change in the various structural layers.
Radius of curvature (R) shows only a very slight increase, which is not unusual.
It should be pointed out though that the level at which it starts off in itself is already low.
It is interesting though that the shape factors (F1 and F2), contrary to the behaviour of the bitumen base pavement and the granular base pavement in particular, showed a decrease in value with the increase in actual repetitions.
The starting values of this pavement in the equivalent granular behaviour state.
is more than those of the granular base towards the end though.
In line with the reasoning for the other pavement types earlier.
the conclusion must be drawn that the deflection basins are becoming
less peaked or more level.
This line of reasoning is confirmed by the behaviour of the slope of deflection (5D) too.
It started off at a very high value
(±
750), indicating a peaked deflection basin from the start as R indeed indicated.
The rate at which 5D increased with actual repetitions is even less than that of the bitumen base pavement discussed earlier.
This points to the fact that there is some form of remoulding or change in balance of the pavement, becoming a "deep" pavement
(Kleyn et al., 1985).
This would definitely reflect more of the quality of the subgrade, which controls the outer edges of the deflection basin (Tam, 1985).
The deflection basin parameters as calculated for the light structured granular pavement on Main Road 18 near Malmesbury, are shown in Figure 3.7 versus the number of actual repetitions.
As shown at the top of this figure, water did enter this test section.
In general this wet phase leads to quite different behaviour of the deflection parameters as the pavement in this state failed rapidly.
Discussion centres on the dry phase in order to correlate the general behaviour with that of the other pavement structures tested and discussed here.
In Figure 3.7 it can be seen that in the dry phase, deflection
(60 to 6915) showed a general increase with the increase in actual repetitions.
Even 6915 showed a definite increase, indicating that this can be termed a "deep" structure reflecting changes of the subgrade (Tam, 1985).
Maximum deflection (60) also shows an increase relative to 6305 indicating changes in the upper layers too.
In the wet phase 6915 was the least affected due to the effect of a clayey subgrade (De Beer, 1983).
The index parameters, base damage index (BDI) and base curvature index (Bel), which reflect the effect of subbase and subgrade layers (Kilareski and Anani, 1982) showed an increase in value with actual repetitions in the dry phase.
This indicates a lowering of the effective elastic moduli of these layers.
The
Z
IL.O
oj: o
ILl ILl
Q..I
OIL.
I ILl tJ)0 z
0_ j:O
U
ILl
0 lij:
1Ll«
00::
0,10
0,05
3. 15
MALMESBURY: VALUES RECORDED UNDER 40 kN DUAL WHEEL
DRY WET e!!l
~t
IL.w;;;!
00:: lD_
:::l«« tJ)1 0_
>
ILl
00: 0:: ILl
«:::l a.
0:
O::U tJ) «
40
20
0
,
5
R
A"'

E oS tJ)
0::
ILl t
0,4
ILl x::t
0,2
1Ll«
00::
~~ 0
~
1,0 sa
BDl.
BCl.
0,8
E oS
0,6
z
0 t
O
ILl
I
IL.
ILl
0
0,4
0,2
0
10'
10
3
10
4
ACTUAL REPETITIONS
FIGURE 3.7
DEFLECTION BASIN PARAMETERS VERSUS ACTUAL
REPETITIONS FOR A TYPICAL LIGHT STRUCTURED
GRANULAR PAVEMENT

surface curvature index (SCI) also indicates a lowering in effective elastic moduli of the base layer by the increase in
SCl in the dry phase.
In the wet phase the value of SCl levels off while BDI and BCI even show a lowering of their values.
This is most probably due to plastic deformation or even shear deformation in the base (Van Zyl and Triebel, 1982) and the effect of the clayey subgrade (De Beer, 1983).
The radius of curvature (R), spreadibility (5) and area (A) parameters stayed virtually constant in the dry phase of this test.
The low initial value of R, does however indicate a weak base with less support than with a cemented subbase.
Shape factors (Fl and F2) and deflection ratio (Q) also either stayed constant during the dry phase of the test or were meaningless in terms of any structural changes.
This author believes that the changes in the abovementioned deflection basin parameters only reflect the distressed state of the failing pavement at that stage without any specific reference to structural layers.
The slope of deflection (SO) showed an increase in value during the dry phase of the test.
This may indicate a chanae in the form of the deflection basin, as the SCI values also indicate, in the region of the loaded wheel.
Radius of curvature (R) however does not confirm this behaviour but this may be related to measuring problems (Horak, 1984).
The initial value of SO is higher than that of the typical granular base pavement which indicates that the deflection basin was indeed rather peaked from the start.
This again reflects on the lack of quality of the base and subbase.
The behaviour of the different pavement types is controlled by the behaviour of the individual layers and by the interaction between the layers forming the pavement structure (Freeme et a1., 1986).
The definition of the states of behaviour is given by Freeme (1983).
These states range from very stiff to very flexible as can be seen in Table 3.1.
TABLE 3.1
Definition of statei·bf pavement behaviour
Approximate deflection range (mm)
Pavement behaviour predominantly controlled by high modulus (> 2 000 MPa) layers acting as slabs
Pavement behaviour controlled by layers with reasonably high moduli (> 500 MPa.
Some layers could be cracked but blocks tend to be larger than 2 m in diameter
Pavement behaviour controlled by material in the granular state.
Moduli of loadbearing layers in the range of
200 to 500 MPa (excluding thin surfacing moduli).
Cementitious layers can be further cracked into smaller blocks
Pavement behaviour controlled by materials flexible in the granular state usually with low moduli (< 200
MPa).
Pavements tend to be susceptible to the ingress of water
TABLE 3.2
Ranges for behaviour states
Behaviour
<5
Deflection basin parameter ranges
SD(*l06)
SCI BDI
Very stiff <0,2
<50 <0,01 <0,01
Stiff
Flexible
Very flexible
0,2 to
0,4
0,4 to
0,6
>0,6
50 to
400
400 to
750
>750
0,01 to
0,2
0,2 to
0,4
>0,4
0,01 to
0,1
0,1 to
0,15
>0,15
BCI
<0,01
0,01 to
0,05
0,05 to
0,08
>0,08
Using Table 3.1
the various HVS tests described earlier were classified according to their behaviour states.
It is clear that the Paradise valley test with the bituminous base is still in the stiff behaviour state at the completion of the test.
The granular base test at Erasmia changed from a stiff behaviour state to a
flexible behaviour state after 100 000 actual repetitions.
The cemented base in the equivalent granular state at Hornsnek, changed from a flexible to very flexible behaviour state virtually from the start of the test.
The same description holds for the light structured granular pavement tested at Malmesbury.
The ranges of the various deflection basin parameters that were identified as the most reliable indicators earlier were determined for each of the behaviour states.
It is believed that by looking at more deflection basin parameters than only maximum deflection that a better definition of the behaviour states is possible.
These ranges are shown in Table 3.2 .
In the previous section it was indicated that the granular base or pavements in the equivalent behaviour states were the only pavements that could be classified as being in either a flexible or very flexible behaviour state.
For these pavements identified, the standard relationships between rut and actual repetitions are available.
The rut measurements of these pavements were correlated with the equivalent axle repetitions (E80s) and the measured deflection basin parameters in a stepwise multiple regression analysis.
An exponent of n
=
3 was used in the calculation of the E80 repetitions (Maree et al., 1982).
In the stepwise multiple regression a Rsquare value of at least 0,75 was set or three variables in the relationship for acceptance.
This resulted in a data matrix of 12 by 30, representative values of the granular base pavements in the flexible and very flexible behaviour states.
Relationship 1 •... Rut = 13,696
R2
=
0,79
+
5,698 (F1)
+
4,153 (F2)
Rut = 15,205
Where; Rut, R2
+ 6,002 (F1) + 0,444 (F2) + 3,935 (E80s).
=
0,82; F1 and F2 areas described above, E80s are equivalent 80 kN acles in millions (106) repetitions.
The significance of these relationships is that granular base pavements in the flexible or very flexible behaviour states can be identified and rut can be calculated from deflection basin measurements.
It is also significant that the two shape factors
F1 and F2 which did not correlate well with changes in state or material state the base layer in particular, does correlate well with the permanent deformation behaviour.
Most of the permament deformation in granular bases originate in the base layer (Maree et a1" 1982).
Four accelerated tests with well documented results were selected to calculate deflection basin parameters.
These tests represent typical bitumen base, granular base, cemented base and light pavement structure granular pavements.
The latter three pavement types were in the flexible behaviour state while the bitumen base pavement was in the stiff behaviour state.
Due to the limoted amount of HVS tests analysed the findings reported earlier in chapter 2 were used as reference in the discussion.
It was therefore only investigated to what extent the typical deflection basin parameters confirmed the indications of other researchers.
Considerable more HVS tests needs to be analysed with the proposed deflection basin parameters (Table 1.1). If statistically significant numbers of tests of each pavement type is available it is suggested that a proper regression analysis be done to see which deflection basin parameter correlate the best with important
structuralparameters such as effective elastic moduli with the increase in repetitions.
In spite of the limited survey an attempt was made to make statements about the generalised relations between the deflection basin paramaters and effective elastic moduli changing with the number of repetitions.
In line with findings reported in chapter 2 it can be stated that the index parameters (SCI, BDI and BCI) gave relatively clear indications of their relations with respectively the base, subbase and selected layers and their respective effective elastic moduli changing with the number of repetitions.
Othe r deflection basin parameters gave rather vague relations if any which limits their use at present with this limited survey.
From the results of the various tests and measured deflection basins, it is possible to give a better description of the behaviour states.
It is suggested that not only maximum deflection should be used to indicate in which behaviour state a pavement is, but preferably the index parameters (SCI , BDI , BCI) as indicated in the Table 3.2.
Rut can be calculated from deflection basin parameters Fl and F2 and optionally the E80s too.
This is true for granular base pavements in the flexible or very flexible behaviour states for this small sample size analysed.
The author stronly recommends that in future a larger sample size of tested pavements be analysed in order to broaden the data base facilitating proper statistical analyses.
This will be of particular benefit to possible relationships between deflection basin parameters and structural parameters of individual layers.
With the new data manipulation programmes for HVS data this will in future be a relatively simple operation.
A dedicated and concerted effort will however be needed for the data retrieval of the past tests. This author only sees his role in this regard as having investigated the possibilities for this present purpose.
LITERATURE SURVEY ON MATERIAL CHARACTERIZATION
AND STRUCTURAL ANALYSIS USING DEFLECTION BASINS
PAGE
4.2
3 METHODS INCORPORATING TWOLAYER LINEAR ELASTIC
THEORY
4.1
Methods using up to two deflection basin parameters
4.2
Methods using at least three deflection basin parameters
4. 11
4.20
The full deflection basin can be measured and the various deflection basin parameters give a better description of it. This was discussed in detail in the previous chapters.
The main aim of this thesis is to use such measured deflection basin parameters in the analysis procedure.
In Figure 4.1 the South African mechanistic rehabilitation design or analysis procedure is illustrated ( Freeme, 1983). The pavement class and pavement type description of steps 1 and 2 will not be discussed here , but detail can be found elsewhere (TRH4, 1985a).
In the previous chapter it was shown how the pavement behaviour state can be enhanced by using measured deflection basin parameters.
Step 4 where the pavement layer state is described is also discussed in detail elsewhere (Freeme, 1983). In Appendix B a brief summary is given on how condition surveys enhance this identification of pavement layer state.
The main emphasis of this literature survey in this chapter is to indicate how measured deflection basins can also enhance step 5
(see Figure 4.1). The layer thickness of the pavement can be determined from asbuilt plans or by profile trenching.
In the mechanistic design process effective elastic moduli are fundamental inputs in the analysis procedure in order to ensure that the evaluation procedure in step 6 (Figure 4.1) can be executed successfully.
In South Africa the material classification as outlined in TRH14 (1985b) and TRH4 (1985a) is based on fundamental behaviour and strength characteristics.
This description of materials form the basis for the description of the effective elastic moduli of each material type in a specific behaviour state (Freeme,1983).
Various destructive and nondestructive tests are normally executed to ensure a correct definition of pavement material layers in terms of the effective elastic moduli used in the final nonsimplified analysis procedure.
Measured deflection basins , as a nondestructive testing means, can enhance the confidence in the assigned effective elastic moduli.
In this chapter a detailed description
I.
PAVEMENT CLASS
A, B, C
3.
2.
"
PAVEMENT TYPE
GRANULAR BASE
BITUMINOUS BASE
CEMENTED BASE
CONCRETE
,
PAVEMENT STATE
VERY STIFF
STIFF
FLEXIBLE
VERY FLEXIBLE
6.
5.
4.
PAVEMENT LAYER STATE
WET, DRY, CRACKED
+
DESIGN INPUTS
LAYER THICKNESS
ELASTIC MODULI
EVALUATION f
CATALOGUE OF BEHAVIOUR
STATES.
MECHANISTIC ANALYSIS
FIGURE 4.1
FLOW DIAGRAM OF THE MECHANISTIC
PAVEMENT REHABILITATION DESIGN
METHOD (FR£EME, /983)
is therefore given given of various analytical methods of material characterization using deflection basin measurements as main input as found in literature.
In the characterization of materials of flexible pavements, various deflection based analysis methods are used.
There are two main groups of methods.
The first group is empirically based procedures with limited information on the full deflection basin and with limited deflection criteria.
The second group uses basic elastic behaviour to determine the material properties.
The majority of procedures in this latter group are based on linear elastic layered theory while the nonlinear elastic behaviour of pavement materials is approximated by using linear elastic layered pavement models or finite element computer programs.
The emphasis in this discussion is on the linear elastic group of methods of analysis.
These procedures use computerized iterative, graphical, tabulated or nomograph solutions to analyse the pavement structures.
In a review of methods using layered elastic theory to model pavements Whitcomb (1982) observed the following common characteristics 
(a) The methods use two to five deflection basin values in the analysis.
(b) These models have two to five layers corresponding with the number of elastic moduli which are backcalculated.
(c) Some of the methods are developed for a specific nondestructive testing device.
(d) There are two basic methods of analysis: computerized iterative solutions and graphical fittings or nomographs.
Whitcomb (1982) also lists the following shortcomings of the layer elastic theory in its application to characterize pavement materials:
(a) An inability to analyse effects of loads at discontinuities
(e.g. cracks and edges)
(b) The validity of the assumptions with regard to interface conditions
(c) Their inability to handle inertial forces or vibrations
(d) Nonlinear stress and strain behaviour of materials (granular materials) .
Of these limitations the last is considered to be the most restrictive.
It is generally accepted that most materials used in pavements, in particular unbound granular materials, exhibit nonlinear stress and strain behaviour.
This leads to the fact that the elastic modulus of such materials is a function of the stress level and the result is that the elastic moduli will change both with depth and lateral position.
Patterson et al.
(1974) states that when there are more than two layers in a pavement, the number of unknown variables increases by three per layer and the system is generally insoluble unless the response characteristics can be defined more fully.
Patterson et al. (1974) also observed that the theoretical models have an inherent weakness in terms of the accuracy in which it can represent the behaviour of the real pavement.
They summarised the expected errors in peak surface deflection to be 30 per cent to +60 per cent when material moduli were measured in the laboratory.
In more vigorous studies the errors were generally reduced to approximately 20 per cent.
Patterson et al.
(1974) noted that another limitation of the deflection influence surface technique is that is not very accurate with regard to the layers very near the surface.
The limitations of the modelling of the loaded areas cause some doubt as to the accuracy of the deflections within an area of 0,5 m of the loaded area.
The discussion on techniques or methods for determining elastic moduli will be divided into two groups.
The first group looks at twolayer models and the second group at threelayer or multilayer pavement models.
Twolayer linear elastic layer theory can be used for preliminary analysis and interpretation of generalized trends.
This may appear to be an oversimplification of more complex pavement structures, but the fact remains though that most surfaced and unsurfaced (low volume) roads have a typical twolayer pavement structure.
This is particularly true in South Africa where surfacings are generally thin (average thickness of 25 mm).
Considerable use is also made of chipsealing.
In analysis methods this thin asphalt layer is often ignored owing to its limited influence on structural analysis.
The twolayered linear elastic model by Burmister (1945) is usually used as the basis for most of these methods.
Yoder and
Witczak (1975) state that the stress and deflection values obtained by Burmister are dependent upon the strength ratio of
E1/E2 of the layers , where E1 and E2 are the moduli of the reinforcing and subgrade layers respectively.
Maximum deflection values for a flexible plate (which represents a tyre load) are determined as follows (Yoder and Witczak, 1975):
00
=
1,5 pa F2
E2 where p a
E2
F2
= unit load on circular plate
= radius of plate
= modulus of elasticity of lower layer
= dimensionless factor depending on the ratio of the moduli of elasicity of the subgrade and pavement as well as the depth to radius ratio
Wiseman et al.
(1977) proposed the simplification of pavement structures by using the Burmister (1945) twolayer system or preferably the Hogg (1944) model. The Hogg model is that of an infinite plate on an elastic subgrade.
Greenstein (1982) used these models for pavement evaluation of lowcost roads.
In
Figure 4.2
falling weight deflectometer( FWD) deflection basin measurements are used to arrive at values of Ep/Es (E1/E2) ) for relative values of pavement thickness to load radius ratio and the specific values of poisson ratio
(v
and
v ).
This nomograph is p s
50,0 100,0
0,1
0,3
6~0
6
0 tJ.
H
1,0
PAYEMENT  E~:i7p : 0, 40
SUBGRADE  E s
,v.
=
°
45
10,0 100,0
Ep
E s
FIGURE 4.2
TWOLAYER MobEL USED FOR
LOWCOST ROADSCGreenstein, 1982)
based on that derived by Wiseman et al. (1977).
Estimate values of El and E2 are reached which may be used as a basis for further analysis.
Berger and Greenstein (1985) simplified the use of the
Hogg model so that it can be used on pocket calculators and deflections as measured with a Benkelman beam.
The general relationship of the ratio El/E2 is used in other graphical or nomographical procedures using the Burmeister model
(1945).
In Figures 4.3 and 4.4, Hoffman and Thompson (1981) show how four deflection basin parameters, 6 , A, Fl and F2, (see Table o
1.1) are related to this basic elastic moduli ratio (El/E2).
These figures were developed for the Falling Weight Deflectometer
(FWD) and Idaho Department of Transportation (IDOT) road raters.
Other similar relationships were developed by Swift (1972) and
Vaswani (1971) for the use of dynaflect deflection basin
In conclusion it can be stated that the elastic moduli based on
Burmister's (1945) twolayered linear elastic theory can be backcalculated with confidence using the deflection basin measurements.
The specific measuring device and deflection basin parameter selected will result in a specific graphical solution.
It is suggested that if this method is used it should preferably be used with granular bases and be treated as a method of estimating effective elastic moduli.
The Hogg model (1944) certainly also proved to be a viable method particularly for cemented or bituminous base pavements.
It should however also be seen as an approximation procedure of more complex pavement structures.
Linear elastic layer theory is widely used to determine effective elastic modulus values of the various layers based on back calculated deflection basin measurements.
Although there are a wide variety of such computer models available with varying levels of sophistication only those relevant to the linear elastic theory
I
~.v
.
, • ....,"""',
I' U"" lOin t201
30 In
N

'0
4 n..
......3
LLI
N
<3 o o
I 2 3·4 5 6 8 10 20 E
I /
E
2
40
0
60 80 100
NOTE: DEFLECTIONSRESULTING FROM FALLING WEIGHT DEFLECTOMETER LOADING OR lOOT ROAD RATER
LOADING MUST BE USED
FIGURE
4.3
VARIATION OF THE "ARE~' AND THE M.AXIMUM DEFLECTION FACTOR
1M IL_T\A/f\I I\VE:"[) I IMC'AD C'I J\~TII" •• nnr::"
I
11.I_.c~ ..I "Tl 
10
.
C

=
<l
LLI a:
=
«
.
+:
\0
2.4
2.2
2.0
1,8
1,6
1,4
It)
<I
<I
I

N
<I u
IJ..N
1,2
1.0
0,8
0,6
0.4
0.2
0
1,4 1,6 1,8 2.0
6
0
6
2
F,
=
6,
FIGURE 4.4
SHAPE FACTORS OF THE DEFLECTION BASIN IN A TWQ LAYER
will be referred to.
Methods using deflection basin measurements or parameters as basic input are discussed briefly below.
Grant and Walker (1972) describe a linear elastic layer theory approach to arrive at effective elastic moduli for a threelayered pavement structure.
The deflection basin parameters <5 and R are used.
Modular ratios of surfacingo overbase and baseoversubgrade are calculated with the CHEVRON computer program and plots in relation to <5 and R are derived, o as shown in Figures 4.5
and 4.6
These relationships were developed for thin surfacings with granular bases, which are typical in South Africa.
Modular ratios of the baseoversubgrade were defined as varying between two and four and the initial estimates of the subgrade modulus was derived from the relationship:
E subgr
=K*CBR where K is a factor varying between 3,5 and 10,3 with the latter used in most cases.
Typical elastic moduli values are fixed for the asphalt surfacings as shown in Figures
4.5
and 4.6 with typ ical layer thicknesses for the surfacing and base layers.
A Poisson ratio of 0,3 was used for the base and subgrade.
Grant and Walker
(1972) therefore conclude that "The above method could be used to obtain an estimation of the subgrade and base moduli for roads with thin asphalt surfacings".
The new Shell Pavement Design Manual (Shell, 1978) forms the basis of the method described by Koole (1979).
The deflection basin parameters maximum deflection (<5) and deflection ratio o
(Q), determined from Falling Weight Deflectometer (FWD) measurements, are used.
A threelayered linear elastic system is modelled.
The pavement structure is characterized by eight variables:
~
I o
..
SURFACING
I
RATIO
BASE
0,3 C
CONSTANT BASE
MODULUS
CONSTANT SUBGRADE
MODULUS
BASE
" SUBGRADE
MODULAR
RATIO
"
"
"
" 64
CALCULATED FOR
SINGLE WHEEL 40 kN
AT 550 kPa
+t + t t h l
=25 mm,
E
1
=2100 MPa
'"h
2
=
300mm E
2
VARIES
E
3
VARIES
0,2 0,5
DEFLECTION
1,0
(mm)
FIGURE 4.5
RE LATIONSHIPS BETWEEN DEFLECTION AND
RADIUS OF CURVATURE FOR CONSTANT BASE
MODULUS, CONSTANT SUBGRADE MODULUS
AND CONSTANT BASE/SUBGRADE MODULAR
RATIO {SINGLE LOADED AREA (Grant and Walker, 1972)
E

1000
I.IJ
D::
:::>
(f)
:::>
25
«
D::
~
D::
:::>
200
0 li
0
100
Ez=KE,
E3 VARIES hz' 230mm
0,1 1,0
DEFLECTION
(mm)
10
FIGURE4.6
PRACTICAL MEASUREMENTS OF DEFLECTION
AND RADIUS OF CURVATURE RELATED TO
THEORETICAL BASE/SUBGRADE MODULAR
RATIOS ( DUAL LOADED AREAS) (Grant and Walker,1972)
Two assumptions are made: Poisson's ratio is taken as being equal to 0,35 for all the layers and the effective modulus of the unbound base layer is a function of its thickness, hZ, and the subgrade modulus E3.
The relationship of Dorman and
Metcalf (1963) is used:
E =k*E
Z 3
o
45 where:
k=O,Z
hZ ' ;
Z<k<4
and hZ is measured in millimeters.
The computer program BISAR is used to prepare a typical graphical chart such as that shown in Figure 4.7.
In this case typical values of E3=100 MPa and hZ=300 mm are used.
The value of h1 is determined from coring results or asbuilt records.
By varying these values of E3, EZ and a resulting E1, deflection basin parameters maximum deflection (0) o deflection ratio (Q ) r and are matched and values of effective moduli are thus obtained.
Koole (1979) states that estimate values of effective moduli for cementtreated bases derived from past experience or measurements should be used as input in the BISAR computer analysis.
The nomograph in the Shell Pavement Design
Manual (Shell, 1978) is a wellknown procedure to determine estimate values of the effective moduli for the asphalt layer.
Snaith et al.
(1980) analyse and arrive at effective elastic moduli for a threelayered pavement structure using the familiar relationship between CBR and subgrade elastic modulus and the relationship between the effective moduli of the base layer
(granular) and the subgrade.
These are the same relationships as those described in the methods proposed by Grant and Walker
(197Z)
and Koole (1979).
Snaith et ale (1980) use the deflection basin parameter, 0 , as o measured with a Benkelman beam.
A simple method of
lO"
8
6
4
N
E
"
2 u
I
(J')
«
::>
0
0
~
LLI
LLI
(J')
«
CD
LLI ..
(J')
10
10
8
6
4
2
10
9
8
6
4
0,90
Q600
\
0,85
RADIUS OF FWD BASEPLATE: 150 mm
Q600:
8
600
18
0
h2 : 300 mm
E2 • 2,7 x
E
3
E
3 :
100 MN
1m
2
F
: 10000 N
v,
So
v2 : v3 : 0, 35 hi
0,55
0,50
0,45
1
70mm
\ 0,40
Q600
0,35
100mm
400mm
150mm
300mm 200mm
2
10
4 6 8 10
2
2 4 6 8 10
3.
MAXIMUM DEFLECTION,
8
0
,10
6 m
FIGURE4.7
DEFLECTION INTERPRETATION
(Koole, 1979)'
CHART
approximating equivalent thicknesses (Odemark, 1949) is used.
The solution consists of two steps:
(a) transformation of the multilayered system into a single layer with equivalent thickness, and
(b) use of the solutions for distributed loads on the surface of a linear elastic semiinfinite mass.
In order to change the layered system into an elastic halfspace the equivalent thickness (H) is calculated for each layer.
e
The principle is that the equivalent layer has the same stiffness as the original layer, so as to give the same pressure distribution underneath the layer.
This results in the following relationship:
~*
1
H =h e
1 E2
*
If the value of the Poisson
I s ratio is the same for both materials, the expression is reduced to: r
1
For a uniform vertical loading on a circular area, the deflection 6 at any depth Z at the centre of the loaded area is o given by
6
z
=(lli)pa[
1
E
(1+(Z/a)2)!
+O2\1)(1+(Z/a)2)!Z/a ]
Estimate values of effective elastic moduli are used as input values to determine the value of 6 , which is compared with the o measured value.
The algorithm to arrive at this value is shown in the sketches in Figure 4.8.
Snaith et al.
(1980) use an electronic calculator to do the calculations and use the criterion of:
16 sur f6 (measured)l< 0,05 (6 (measured» for iterations.
0 o.
After a minimum of three deflection values have been found and plotted on graph paper, it is possible to estimate the required modulus value.
It is not clear from the discussion by Snaith, et al. (1980) whether these deflection values refer to 6 alone, o but this is assumed to be so owing to lack of indications to the contrary.
A check calculation can be done with this estimate value.
It is not clear how the load distribution measured under dual tyres is represented in the calculations.
Snaith, et al (1980) obviously only consider one loaded area.
Dehlen
(1962b) also used Odemark
I s approximate solution for a multilayered system.
Dehlen (1962b) states that; "Because of doubtful validity of Odemark' s theory away from the axis of load, no attempt was made to compute deflections or curvatures between dual wheels and, in the case of such tests, computations were made simply for a single circular load of the same area as the dual wheel imprint.
II
The results of such computations are shown in Figure 4.9.
Dehlen (1962b) further indicates that differences exist between Elastic Theory and practice, mainly in that deflections are more concentrated about the load than indicated by theory, and that they decrease more rapidly with depth.
Molenaar (1983) analysed a threelayered linear elastic system using measurements taken with a falling weight deflectometer
(FWD).
Molenaar (1983) also makes use of Odemark
IS
(1949) equivalency theory.
He states:
II the equivalent layer thickness is a magnitude which is meaningful and easily understood.
A pavement with a high H will last longer than a e pavement with a low H ".
The equivalent layer thickness (H ) e e is determined as follows:
8 surt
I
Mr.
2
8surt:8subg
+C
2
+C
1
C
2:
H
2 
H
2
I
C
I
=
HI HI
,
." o
I:D
0\
"o
U)
"If
I
~
"
I
~~~_
••••••••

////
//
/
." 7 ,'//
////////
( b) Equiva lent sUbgrade thickness layer
~
°2
I
(c) Equivalent unbound thickness layer
FIGURE 4.8
COMPONENTS.
OF A SURFACE DEFLECTION
( Snaith , e tal., 1980)
..

(J) w x
~ ,100
LL
W

l
~ 500
/'
}A~
/~
MEAN LINE, o SLOPE
=
1,61
(J)
~ ,080

MEAN LINE,
0/ ,,'
x
;x"
A "
,/
0/
SLOPE ~
0
~
>
~ 400
o
lL
MEAN LINE,
SLOPE 1,71~/ o
/0
frl
'0
~ 300
/
LL
W
a a ;040
w
I
09" ; rl6
0 ""'
Y
MEAN LINE,
/0;" SLOPE=.71
~
0:: 200 a w
~ ,020
:E o
o
~
L"/
'/
o
,020 ,040 ,060 ,080 ,100
~
Q.
:E o o
100 o ~" x/'/o9.°
0 50 100 150 200 250
OBSERVED DEFLECTIONS(I NCHES) OBSERVEDRADII OF CURVATURE(FT)
 0
MEASUREMENTS MADE BETWEEN DUAL WHEELS
COMPUTATIONS FOR SINGLE LOAD OF SAME AREA
XMEASUREMENTS AND COMPUTATIONS FOR SINGLE WHEEL
FIGURE 4.9
COMPARISON OF OBSERVED AND COMPUTED DEFLECTIONS
AND RADII OF CURVATURE (Dehlen, 1962 b)
H e
=
0,9
Ll
I: . 1
1.= where h.
1.
= thickness of layer i in meter
E.
1.
E s
L
= elastic modulus of layer i in N/m2
= elastic modulus of the subgrade in N/m2
= number of layers.
Using the deflection basin parameter, surface curvature index
(SCI), relationships between the SCI and versus Hare e determined as shown for various subgrade moduli (E ) in Figure s
4.10.
This is for a threelayered pavement structure.
The subgrade modulus is also calculated directly from the falling weight deflectometer (FWD) deflection basin as follows: log E s
=
9,87  log 6 r where r in mm.
=
2 meters from the loading centre and 6 is measured r
(The load force is 50 kN, loading time .is 0.02
second) .
Elastic moduli of the various layers can thus be backcalculated, if the layer thicknesses are known, using a dure similar to that described by Snaith et al.
(1980) , and using the general moduli relationship between base and subgrade and the Shell nomograph procedure as described by Koole (1979).
For a more effective use of the whole measured deflection basin in the determination of effective elastic moduli, at least the same number of deflections should be used as the number of layers in the pavement structure.
This general approach is described in a FHWA report (1984).
Normally a maximum of five deflection basin measurements extending radially away from the centre of loading are used.
In Figure 4.11
a fourlayered elastic system is illustrated.
When a load of known intensity is applied over a known area, deflections are created at some distance from the centre of the loaded area.
It is normally
0:: w
J:
••••
E


Q)
J:
..
en en
w z
~
U
2,0
1,0
SUBGRADE
ELASTIC
MODULUS
0,8
w
~
::>
0 w
0,6
2 4 10
2
2 4 r
SURFACE CURVATURE INDEX, S CI
(,urn)
=
500 mm
FIGURE 4.10
RELATION BETWEEN THE
SURFACE CURVATURE INDEX
(SCI> AND THE EQUIVALENT
LAYl;R THICKNESS (He>
(Molenaar, 1983)
r1 =0
I
I
<t
I
LOAD
+8
1
"
SURFACE DEFLECTIONS
t
2
8
3
,8
4
r2 r3
"
"r4
"
"
"
"h,
1/1
E t h
2
1/2
E2 h
3 1/3 E3
CO
1/4 E4
FIGURE4.11
FOUR LAYER ELASTIC REPRESENTATION OF A PAVEMENT
SYSTEM (FHWA,1984J
assumed that the load is distributed through the pavement system by a truncated cone (as shown by the dashed line in Figure
4.11) .
Based on this concept, the deflection 64 at a distance r4 from the centre of the load is due to the "elastic" compression of layer 4 since layers 1,2 and 3 are outside the influence cone created by the load.
Likewise, the deflection 63, at distance r3 is due to the compression of layers 3 and 4; the deflection at distance r2 is due to compression in layers 2,3 and 4 and the deflection 61, is due to compression in all layers.
Thus by backcalculating one should work radially inwards from 64 at r4 towards the centre of loading in matching calculated deflections with measured deflections.
This will result in the determination of effective elastic moduli of deep layers
(subgrade) first and then of the other layers progressively upwards to the surface layer.
Using road rater data Kilareski et al. (1982) expressed this as follows:
61 ~ f1 (E1, E2, E3, E4)
62 ~ f2 (E2, E3, E4)
63 ~ f3 (E3, E4)
64 ~ f4 (E4)
This forms the basis of the successive approximation procedure.
Estimate or seed values, as discussed preViously, are assumed to start the iteration process.
Using the BISAR computer program,
1 1 1 1 the deflection values 61, 6
2,
63 and 6
4 corresponding to the assumed values of moduli are calculated.
These calculated values are compared with the measured deflections, 61> 6
2,
63 and 6
4 at the measuring points as shown in Figure 4.11.
The correction method of the effective elastic moduli E.
is
J.
E. new
J.
=
1E. old (6~ + 6. /6.)
J.
J.
J.
J.
The corrections are made to the subgrade first (E4 and o~.
04 values) and a new deflection value is determined after which E3 is 'adjusted and then EZ and lastly E1 by calculating the new corresponding deflection value
(0:) each time.
This completes
1 one iteration after which the process is repeated until the following criterion is met:
Error.
1
=
[0.
1
1

1
0.
1 o~j
*100 where Error1 =
5 per cent allowed for 01
1 and ErrorZ and
Error3 and Error4
= 1 per cent allowed for 01 01
Z
3
1 and °4·
This is all done by an interactive computer program developed by
Anani (1979).
With regard to the uniqueness of solutions.
Kilareski et ale
(198Z).
state that unique values of E4 can be determined from 04 calculations and similarly unique values of E3 from 03 calculations.
In order to ensure unique values of EZ and E1 from
0z
1 1 and 01 calculations, a certain range of E1/EZ ratios was assumed initially.
This value was chosen as 0,7 as determined from laboratory resilient modulus testing on core samples.
MODCOMP I is a computer program developed by Irwin (1981) to interpret the moduli of elasticity of pavement layers from surface deflection data.
The program can handle up to eight layers in the pavement using the CHEVRON nIayer code.
Up to six surface deflections measured on the deflection basin are used.
Measurements with vibration or impact devices are preferred in order to exclude plastic creep associated with
Benkelman beam measurements.
procedure is quoted as follows:
The principle of this analysis
"At large radial distances the surface deflections are primarily the result of deformation in the deeper layers.
Thus.
the
magnitude of the moduli of shallow layers has very little influence on the surface deflections of the pavement at large distances from the load." The back calculation procedure is then the same as that described by Kilareski et al. (1982).
Seed values or estimate values of elastic moduli are used as input.
An interesting feature of this approach is that the deflection basin measurements are first interpolated with a curvefitting subroutine (CRVFIT).
This is done so that there are measured deflection values, corresponding radially to a
38degree cone intersecting the pavement layer interfaces as shown in Figure 4.12.
No reason for the choice of the
38degree cone is given.
Adjustments to the modulus of the layer underneath the relevant interface are made using the following equation:
Enew = Eseed (1+2 t
6i
:i
6 ij)
'7, where
6i
= calculated deflection at the ith radius
6.
= measured deflection at the ith radius.
1
The factor 2 is used to accelerate the iteration process, but
E new is not allowed to become negative.
Using the E new value
(all other values unchanged) the deflection at that point is recalculated.
A linear interpolation is then made in loglog space so that a value of the modulus for the layer, E. t
1n erp.
is obtained, based upon the measured deflection.
From sensitivity analysis data, Irwin (1981) suggests that the tolerance level for computation purposes in MODCOMP I be five to ten times lower than the standard error of the measurement system (+ 0,02 rom).
The principle of modulusatdepth as a function of the distance from the loaded area of the deflection basin is also the basis of the method used by Patterson and van Vuuren (1974).
The use of the surface deflection basin is seen as a first method of determining effective elastic moduli.
Deflection basin measurements were obtained with a modified Benkelman beam with a
hI
LAYER
1 h
2
LAYER 2
"
""
" h
3
LAYER 3
CONEI LAYER INTERFACE INTERSECTIONS DEFINE RADII
FOR CALCULATIONS r4
DISTANCE FROM LOAD
I
I
I
I
+r
I
I
I
I
I
+ 
I
I
I
I
I
I
I
I
I
I
MEASURED
DEFLECTIONS
FIGURE 4.12
DEFLECTION BASIN SHOWING MEASURED
DEFLECTIONS AND CRVFIT SUBROUTINE
INTERPOLATIONS ( I
rw
i
n
J
1981 )
deflection transducer for a "continuous" output.
Layer thicknesses and material estimates were used as input in a trial and error process using the CHEVRON and ELSYM programs.
The same basic approach as described by Irwin (1981) and Kilareski et al.
(1982) was followed to determine and fix effective elastic moduli values by using deflection basin values contracting radially.
Figure 4.13
shows a typical result of matching measured and calculated deflection basins and derived effective elastic moduli.
Husain and George (1985) use the CHEVRON program to do deflection matching.
The measured deflection basin of either
Dynaflect orfalling weight deflectometer (FWD) can be used.
The deflection equation is inverted by a nonlinear pattern search technique to determine the values of the layer moduli that would best fit the observed surface deflections.
The elastic modulus of the asphalt concrete layer is corrected for temperature and the base and subbase moduli are corrected for stress dependency.
The algorithm used, starts from the surface layer and proceeds to the subgrade.
A general gradient technique is used' in order to minimize the sum of squared errors.
The principle of deflection at distance from load applied being a function of material characteristics a~so forms the basis of the model used by Marchionna et al.
(1985) • In general the model is as follows; where o.
= deflection relative to the point located at distance r.
1 1
C~,J
=
Jth mechanical characteristic of the material relative to the Kth layer
SK
= thickness of the Kth layer
F = load applied
The falling weight deflectometer (FWD) is used with seven measuring positions and an elas~ic four layered pavement
....
E
:l.
100 z
Q
~ u
UJ
..J
~
UJ
0
200
300
UJ
U
It a:
::>
IJ)
400
500
DERIVED DEFLECTION
PROFILE ()
OBSERVED DEFLECTION
PROFILE ()
E (MPa) tJ h (mm)
1000 0,20
200
0,3S
250
150
150 0,40
300
60 0,35
2000
DERIVED PROFILE USING A SINGLE
CIRCULAR LOAD PER WHEEL ()
200 0,3S 00
FIGURE 4.13
SIMULATION OF LONGITUDINAL SURFACE DEFLECTION
INFLUENCE LINE AND DERIVED MODULI
(Patterson and van Vuuren, 1974)
elastic in this model, but granular bases and subbases and subgrade layers are treated as nonlinear elastic.
The analysis is carried out with the method of finite elements and the
Nonlinear Structural Analysis Program (NONSAP), developed at the University of California, is used.
Various subroutines were added in order to use a technique of multiple regressions to find the expression of the 0.
functions that best interpreted l.
the data available and met the conditions described.
The method of equivalent thicknesses described by Odemark (1949) forms the basis of the procedure described by Ullidtz and
Peattie (1982).
Surface deflections are measured with the FWD at the centre of loading (0 ) and a minimum of two other
0 positions
(01' and 02)'
It is specified that
02 be measured at a distance
(radially from the load centre) of at least five times the load area radius (a)j it must also be more than the thickness of the equivalent layer thickness (H).
e
The latter is calculated in accordance with the,description by Koole
(1979).
He gives the reason for the distance specification is that "at large distances the surface deflections are approximately inversely proportional to the modulus of the subgrade".
Layer thicknesses are determined by coring and estimated values of elastic moduli are assigned to each layer.
Values of surface deflections are calculated by using computer programs like BISTRO or CHEVRON, or Finite element method programs.
Ullidtz and Peattie (1980) suggest the use of programmable calculators using the equivalent layer thickness approach.
The equivalent surface modulus E (the modulus of the halfspace o that would give the same surface deflection as the multilayer structure) is calculated as follows at corresponding distance r2 where
02 is measured :
(1\1
2)
P a
2) r
2 02
where the symbols are as previously described by Snaith et al.
(1980) for the twolayered pavement system.
For the prescribed value of rZ the equivalent surface modulus (Eo) is approximately equal to the subgrade modulus.
The subgrade estimate modulus
1 value is adjusted and the value O
2 is calculated and compared with the measured value O
2,
The stiffness of the asphalt layer is determined using the ratio
1 of the deflections 00' This ratio is highly dependent on the stiffness of the upper layer.
If the calculated value of the ratio is less than the measured value, the estimated value of the stiffness of the asphalt layer must be increased because a high ratio corresponds with a high stiffness in the asphalt layer.
The stiffness of the intermediate layer (normally granular) is determined from O.
o
Stubstad and Harris state that the latter is the least accurate value.
(1984)
Laboratoryderived ratios pf tolerances or guides.
Some
E1/EZ
of and these
Ez/E3
are relationships used used as by
Shell and described by Koole (1979) are also used.
In the later versions the program ELMOD on the HP85 microcomputer are used to analyse a fourlayered pavement structure.
In this program higher precision was reached if the following conditions were met:
(a) The structure should contain only one stiff layer; if there are more they should be combined into one layer for the purpose of structural evaluation
(b) Moduli should decrease with depth
(c) The thickness of the upper (stiff) layer (h1) should be greater than half the radius of the loading plate
(aIZ)
(d) When testing is done near a joint or a large crack or on gravel roads, the structure should be treated as a twolayer system.
Nonlinearity of materials was also accommodated for by using a mainframe computer program ISSEM4 which can model a fourlayer
pavement.
Ullidtz (1982), however, gives guidelines on how to accommodate stress softening (nonlinear) subgrade layers by constructing diagrams based on calculations done with finite element computer programmes.
This was done for a twolayer system but formed the basis of the iteration process to determine moduli values for the subgrade.
Adjustments' were made for temperature, time of loading and other environmental influences throughout the year.
These were built in as standard features of the ELMOD program described above.
In conclusion on this method Epps and Hicks (1982) state that:
"The method proposed by Ullidtz and Peattie (1980) comes closest to a "universal" technique, but required the use of a computer.
As the capabilities of small computers increase and as their use becomes more widespread, this requirement will be less and less of a deterrent to its use."
Stubstad and Corner (1983) made use of this latter method using the FWD to predict damage potential on Alaskan highways during spring thaw.
The similarity with stabilized subbases is illustrated by their statement; "... it was immediately noticed that the same tendency toward virtually no deflection at large distances from the FWD load was occurring during the early spring of 1982.
Such a phenomenon can only occur if the underlying layers have a high stiffness or modulus of elasticity.
It was thus decided to use layered elastic theory to determine the effects of thaw depth and other material characteristics on the seven FWD deflections."
Bush (1980) developed an evaluation procedure for light aircraft pavements based on a layered elastic model.
The CHEVDEF program used was developed to determine the set of modulus values that provide the best fit between a measured deflection basin and a computed deflection basin when given an initial estimate of the modulus values, a range of modulus values and a set of measured deflections.
Deflections were measured with the Model 2008 Road Rater.
Two force levels were used (5 000 and 7 000 lb) in order to predict the nonlinear
stressdependent behaviour of the subgrade material.
Results from the CHEVDEF program gave the relationship for the deviator stress and the modulus for the subgrade materials.
Thompson and Hoffman (1983) used the ILLIPAVE computer programme to develope deflection basin algorithms for conventional flexible pavements and full depth asphalt concrete pavements.
The effect of nonlinearity of the subgrade of such three layered pavement structures is taken into consideration.
Tam (1985) use the same approach as Kilareski, et al. (1982) to calculate effective elastic moduli by relating the deeper layers to the outer defelctions.
Thus by fixing effective elastic moduli from the bottom upwards, deflections are fitted radially inwards.
Tam (1985 ) however make use of the BISAR or BISTRO computer programs rather than CHEVRON.
The reason is illustrated in Figure 4.14
where the calculated deflection basins for the specific pavement structure and loading conditions are shown as calculated by BISTRO and CHEVRON.
It is clear that the CHEVRON program has a slight discrepancy in the area between the edge of the loaded wheel and
+
400 mm from the centre of loading.
This tendency was confirmed by Taute et al.
(1981) on stiffer pavement types, too.
The discrepancy is more pronounced on lighter flexible pavement.
Before the iteration procedure is applied with the typical linear elastic approach, Tam (1985) takes the nonlinearity of the subgrade into consideration.
This is done by subdividing the subgrade into rather thick layers (0,6 to 1,0 m).
The effective elastic modulus of each layer is then calculated as follows:
350
~
o
0,2
DISTANCE FROM LOAD CENTRE (m)
0,4 0,6 0,8
E
::t.
lLJ
U
it
a::
:;)
(J) z
Q
Iu lLJ
...J
l.L
IJJ
0
600
650
700
750
800
850
900
950
1100 kPo
(CONTACT PRESSURE>
KEY: x BISTRO o CHEVRON
::1 t r =160mm r
E=5000 MPo, u =0,4
l
40 mm
FIGURE 4.14
·COMPARISON OF DEFLECTIONS CALCULATED BY.
BISTRO AND CHEVRON PROGRAMS
(Tom
I r985)
I p~ r where E is the elastic modulus (MPa) pI is the initial effective everburden stress (MPa) o q is the deviator stress due to applied load (MPa)
A is the amplification factor (MPa)
B is the nonlinear power coefficient.
The seed values of A and B are selected as 50 MPa and 0,2.
By us ing the deflection measured at a distance of I,2 m from the load centre, A is first adjusted and then B.
When all the subgrade layers have been fixed, the normal iteration procedure, as described earlier, starts.
Estimate values of effective elastic moduli, based on laboratory and field observations, form the basis of the majority of back calculation procedures discussed.
The mechanistic procedure used in South Africa forms a excellent basis for these estimate values of effective moduli as discussed.
It is believed that by extending the field observations, in particular the HVS tests, this initial estimation procedure can be refined even further.
The analysis procedures have been described at length and for this reason only recommendations related to the South African position will be made.
The linear elastic layered computer programs currently in use in South Africa are capable of backcalculating effective elastic moduli values from deflection basin data.
Normally there is a maximum of five layers, which require at least five deflection measurements extending radially away from the centre of loading.
Various researchers have suggested that the basic relationship of deflection measured radially from the load centre is a function of the various individual layers or combinations thereof.
Some have even suggested an angle of intersection
of the interfaces of layers in depth to determine optimal deflection measuring points radially.
It is clear from the methods discussed that the reiterative backcalculation procedure should work radially inwards to match calculated deflections with measured deflections.
This would result in the determination of effective elastic moduli for the surface layer.
It is evident that this approach focuses on the ideal linear elastic condition and that factors like nonlinearity, nonuniformity and stress dependence are mostly ignored.
Finite element method computer programs are becoming more readily available and can be used; nonlinear models can also be investigated.
It is suggested that correlation studies should be done for each type of pavement in order to establish these relationships.
Methods to accommodate the nonlinearity of the subgrade with the linear elastic computer models available exist and can be investigated.
In none of the methods discussed was much emphasis placed on cementitious bases and subbases and their analysis procedures.
It is believed that enough information from HVS tests is available to analyse these pavements accurately with linear elastic layered computer programs.
This would include, for example, information on the various stages of cracking of these layers.
This also stresses the need for the analysis procedures to be related to the pavement category or class and behaviour state.
As was suggested in Chapter 3 the vast amount of information gained from RSD and MDD results makes it possible to calculate effective elastic moduli by various means for various pavement structures, loading conditions, moisture conditions and equivalent axle repetitions.
This may lead to extensive regression analyses done in order to relate deflection basin parameters for the suggested pavement classes to the structural conditions related to structural life and behavioural states.
Serious consideration and analysis should be given to incorporating methods based on Odemark's (1949) equivalent layer thickness theory.
It has proved to be a method that can satisfy mechanistic design method criteria.
In order to establish this, extensive regression analyses need to be done with the abovementioned available data.
EllECTIVE ELASTIC MODULI DETERMINED FROM
ROAD SURFACE DEFLECTOHETER MEASUREMENTS
2
3
EFFECTIVE ELASTIC MODULI CALCULATED FROM DEPTH
DEFLECTIONS
EFFECTIVE ELASTIC MODULI CALCULATED FROM SURFACE
DEFLECTIONS
3.4.1
Assuming linearity of the subgrade
3.4.2
Assuming nonlinearity of the subgrade
5. 11
5.14
Deflections are measured on the surface and in depth of a pavement when tested with the accelerated testing facilities, the Heavy
Vehicle Simulators (HVSs).
In the past the deflections as measured in depth with the MultiDepth Deflectometer (MOD) were used to determine the effective elastic moduli of the various layers with satisfactory results.
The whole deflection basin, as measured on the surface with the Road Surface Deflectometer (RSD), was always available for determining effective elastic moduli.
The method whereby effective elastic moduli are determined with the
MOD is briefly described.
The author proposed a new method for determining effective elastic moduli from measured RSD deflection basins which is described in detail.
The effective elastic moduli determined from RSD and MOD deflections from selected accelerated tests are compared and conclusions drawn from that.
The nonlinearity of the subgrade is investigated by determining the effective elastic modulus by means of the proposed method and comparing the results with the normal linearelastic approach.
Deflections are measured at various depths within the pavement structure as a standard procedure (Freeme et aI, 1982) on sections tested with the accelerated testing facility, the Heavy Vehicle
Simulator (HVS).
The deflections are measured with the MultiDepth
Deflectometer (MOD) (Basson et aI, 1980).
Measurements of resilient deflections with depth are taken throughout the test under various wheel loads and these yield a good record of the change in structural response of the pavement.
Effective elastic moduli are calculated from these MOD deflections
(Maree et aI, 1981) by using linearelastic theory and a linearelastic layered computer program such as ELSYM5 iUniversity of California, 1972).
The iteration procedure whereby moduli values of the various layers are estimated and the measured deflections in depth are matched by the calculated deflections, is illustrated in
Figure 5.1 (Maree et aI, 1981a).
The procedure is illustrated for a
40 and 70 kN wheel load.
The slope of the depth deflection curve
DUAL WHEEL LOAD
=
40 kN
I
~
Q..
w a
E
400
E
500
600
700
0
100
200
DEFLECTION (mm)
0.1
0.2 0,3 0,4 0,5 0,6 0,7 0.8
0,9
IjO
SURFACING
CRUSHED STONE
BASE
CEMENTED SU8BASE
300
SELECTED SUBGRADE
SUBGRADE/FILL
800
900
1000

LEGEND:
0
MEASURED DEFLECTION
 EBASE
=
450 MPa; ESUBBASE: 3500 MPa
_._._EBASE
=
450 MPaj ESUBBASE: 600 MPa
EBASE
=
200 MPaj ESUBBASE: 500 MPa
DUAL WHEEL LOAD
=
70 kN
E
E
I
~
Q..
w a
400
500
600
700
DEFLECTION ( mm )
0 0.1 0.2
0.3
0.4 0,5 0.6 0,7 0.8 0.9
1.0
I
100
CRUSHED STONE
BASE
200
300
CEMENTED
SUBBASE
SELECTED
SUBGRADE
800 SUBGRADE/FIL L
900
1000
/
LEGEND:
o
MEASURED DEFLECTION
E BASE: 300 MPa i
E SUBBASE:500 MPa
FIGURE 5.1
MEASURED AND CALCULATED DEPTH DEFLECTIONS (ROAD P 157//J
w
.
U1
at any point is an indicator of the modulus of the material at that depth.
This manual method of adjusting moduli values was automated (Coetzee and Horak, 1981) using the CHEV4 computer program (Abbot, 1977).
This program was later adjusted to handle up to 15 layers (Coetzee,
1982).
The moduli determined from the depth deflections are used as input values for further detailed mechanistic analyses of the pavement structures tested (Maree et aI, 1981b).
The full deflection basin can be measured on the surface of a pavement.
using the WASHO procedure (Monismith.
1979).
This is measured on HVS test sections with the Road Surface Deflectometer
(RSD) (Basson. 1985).
In the past only the maximum deflection and radius of curvature were calculated from RSD data.
Recently better use was made of the full deflection basin by calculating other deflection basin parameters too (Horak. 1985).
In order to make use of the measured deflection basins more effectively.
various researchers have used the full deflection basin to calculate effective elasti moduli (Horak. 1984).
In such a procedure to determine effective elastic moduli from surface deflections.
at least the same number of deflections should be used as the number of layers in the pavement structure.
In Figure 5.2 it is illustrated how the measured deflections, from the surface deflection basin. are used in a typical fourlayered elastic system.
It is assumed that the load is distributed through the pavement system by a truncated cone intersecting the pavement layers at an angle (a).
Based on the concept of linear elasticity. deflection 04 at a distance r4 is due to the elastic compression of layer 4 while deflection 03 at distance r3 is due to the elastic compression of layer 3 and 4.
The result is that maximum deflection 01 in Figure 5.2. is due to the deflection of the effective elastic moduli of all the layers (01
= f(E1,
E
Z'
E3,
E4)·
LOAD
<t
I
I
I
I r2
"
"'
"'
"
"", r3 r4
"",
'"
'"
""
"'"
CO h
3 h
2 hi
FIGURE 5.2
FOUR LAYER ELASTIC REPRESENTATION OF A PAVEMENT
SYSTEM (FHWA,1984J
In the backcalculation procedure the effective elastic modulus of the subgrade (E4) is calculated first by fitting the deflection at distance r4 to the measured deflection 04, Then follows the calculation of E3 by calculating and fitting the deflection at distance r3 to the measured deflection 03, Effective elastic moduli are therefore calculated from the lower layers upwards by fitting the deflections radially deflection.
The BISAR computer program (Horak.
1985) is used in this backcalculation procedure because of its superior accuracy in the vicinity of the loaded wheels (Tam.
1985).
Estimate or seed values of elastic moduli are initially assumed for all the layers based on material information.
asbuilt information and material type.
These seed values are then adjusted by comparing the calculated deflection with the respective measured deflection at that point considered.
This adjustment procedure is done in two phases.
The first phase makes use of an interpolation procedure to save computer time.
The second phase uses these calculated effective elastic moduli as input or as seed values and calculates the effective elastic moduli more accurately.
In Figure 5.3 the flow diagram of the first phase of adjustment is illustrated.
The deflection (0.seed1).
as calculated from seed
1 values (E.seed1 )• is calculated and compared with the measured
1 deflection (o.meas.).
A tolerance of 5 ~meter
1
(0.005 rom) is used to decide whether an adjustment is necessary.
If there is an a d· t men t necessary..
E Calc.1.
1
1S lId h Th e f t
2 in the calculation is used to deliberately overcompensate.
The
BISAR program is run again and now a linear interpolation is used in a loglog space (deflection versus modulus) as indicated in
Figure 5.3.
The value E.interp. is now used as the new seed value
1 in the calculation and adjustment of the other layers in phase 1 until all the layers are adjusted in such a way.
In phase 2 the seed values of the elastic moduli are those calculated as E.interp. in phase 1.
This is illustrated in Figure
1
81SAR
INPUT,
Ejseed, I
LEAVE
E.seed,1 =E.seed,2
I I j
= n
I ; n=LAYER
NUMBER
E.COIC,2=E.seedjl
I I
(
1+2
.
[8.C01C
I
,,+
8~eOS])
I c;:,..meos
~I
()
I
<T
I o
.•..
() o of)
~
NEXT
LAYER
CHANGE
E,interp = E .seed, 2
I I
8.
I
OUTPUT calc, 2
Log Ejinterp=
(L09E'lseed,I_L09E\.COIC,1
.
Log 8jcolC,I Log 8jCo1C,2
) Log 81·meos
+LogEjseed,I+LOg8jColc,1 (L09EjSeed_L09EjCOIC
Log 8jCOIC,I_ Log 8 j
COIC;2
)
FIGURE 5.3
FLOW DIAGRAM OF PHASE I OF PROGRAM 81SFT
BISAR INPUT, E j seed, 2
LEAVE
E.
seed,2
I n i
= nI ;
= LAYER
NUMBER
NEXT
LAYER
Ej colc,2
=Ej seed,2
( ~'I
8 j
COIC,I) meos
OUTPUT
8j calc, 2
E. calc, 2
I
=
E. seed,2
I
8.
colc,2
I
=
8.
colc,1
I
·
The deflect10ns calculated (6.
1 calc 1 ( meas. )
') and measured 6.
1 are checked against the specified tolerance of 5 ~meter in order to adjust as indicated.
Each layer is adjusted in the sequence as discussed earlier.
A maximum of 5 total iteration loops are allowed at this phase to limit computer time.
An iteration loop is seen as the adjustment of all the layers.
As the adjustment of effective elastic moduli of the layers near the surface are more difficult to determine and more costly in terms of computer time (Tam, 1985) an option to fix the effective elastic modulus (E.Seed ,fixed) was built into the program.
In
1 general the material information, asbuilt information and knowledge of these layers are such that the material can be classified accurately (Freeme, 1983).
The nonlinearity of the subgrade is not considered yet in the BSFT backcalculation program.
This can however be done manually beforehand.
The mechanistic design and analysis procedure in South Africa does not yet accommodate the nonlinearity of the subgrade.
The backcalculation procedure of the MDD inherently makes use of a nonlinear approach though.
With the assumption that deflection at a depth of 2 meter (where the MDD is anchored) is zero, it is implied in the backcalculation procedure that below 2 meter there exists a semiinfinite rigid layer or a layer with a rather high effective elastic modulus.
The approach that is suggested, is based on the procedure described by Tam (1985).
The subgrade is subdivided into four layers with thicknesses of 0,6 m, 1,0 m, 1,0 m and 2,0 m respectively, overlaying a semiinfinite layer.
The BISAR computer program is then used to calculate effective elastic moduli at middepth of each layer and 2,0 m into the semiinfinite layer.
The seed values for the effective elastic moduli as derived by means of BSFT are used as input for the other structural layers.
The deflection at distance (n1)305 mm (where n is the number of structural layers) from maximum deflection (6 ) o is first checked for nonlinearity.
This will be 1220 mm for a
a five layered system.
If the measured deflection (6~220) differs more than 0.005
mm from the calculated deflection (6~220)' nonlinearity is assumed in the subgrade.
The seed effective elastic moduli of the subgrade layers are then altered by using the equation below as derived by Brown (1979);
E subg.
=
A
P o
1B where E is the sugrade layer effective elastic modulus (MPa) p1 is the initial effective overburden stress (MPa).
0
11 1
(p
=
/3 (0 1
+
2(0 3
»
0 q is the
(q
= deviatoric stress due to applied load (MPa).
0
1 1
1 
0
3)
A is the amplification factor (MPa)
B is the nonlinear power coefficient
0
1 1
1 and
0
3 are effective major and minor principle stresses
(MPa)
In the iteration procedure.
the value of A is taken as the subgrade effective modulus as determined in the linear BSFT program.
The value of B is taken as 0.2 as suggested by Tam
(1985).
In a typical fivelayered pavement structure.
the deflection at 1220 mm (61220) is used to adjust the value of A first. using:
=
A. (
6 c)
J. 
6 m where Ai and Ai+1 are the ith and (l+i)th iterative value of A
6 c and 6 m are the calculated and measured deflections
With the new value of A and the same value of B.
a new set of subgrade effective elastic moduli are computed.
The effective elastic moduli of the other structural layers are kept the same.
This process is repeated until the difference between the measured and calculated deflections at 1220 mm is less than 0,005 mm.
The deflection at n*305 mm, which is 1525 mm for a 5 layered system, is then used for comparison purposes.
The nonlinear power coefficient, B, is then adjusted as follows:
B i
+
1
=
B i ( d c
+
<5 m)
2<5 c where Bi+1 and Bi are the (i+1)th and ith iterative values of B and d and
<5 are the calculated and measured deflections at 1525 c m mm from load centre.
This process of adjusting Band th effective elastic moduli of the subgrade layers is repeated until the criterion of 0,005 mm deflection difference is satisfied.
Effective elastic moduli were determined from selected pavement structures as tested with the accelerated testing facility, the
HVS.
The layer depths are known and the effective elastic moduli had already been determined in some cases using the depth deflections from the MDD.
The effective elastic moduli were calculated using the measured surface deflection basin data as described in Section 3.2.
The angle a, shown in Figure 5.2 was taken as 38° as standard after a was varied between 30°, 45° and
60
0 •
The value of 30
0 was found to give effective elastic moduli that were better related to those determined with the MOD measurements.
This is however also a function of pavement type and material type.
The wheel load used in the calculations was 40 kN with a 520 kPa tyre pressure.
In Table 5.1
the calculated effective elastic moduli are shown for a typical granular base pavement tested at
Erasmia (Horak, 1986a).
The effective elastic moduli as determined from MOD and RSD measurements are shown for each structural layer at various repetitions.
In order to compare the effective elastic moduli determined with the two measurements, the modular ratios (RSD method/MOD method) are
also shown.
A modular ratio of about 1 would indicate nearly the same effective elastic moduli as determined by both measuring techniques.
The BSFT backcalculation program uses increasingly more time to calculate effective elastic moduli nearer to the surface.
This is related to the calculation procedure as outlined in Section
3.2 and the difficulty of achieving the specified accuracy.
In order to save computer time, the effective elastic moduli of the surfacing and the granular base layer were fixed.
The fixing was based on other material information and prior determined effective elastic moduli with MOD deflections.
Actual repetitions
Layer description
Base
Subbase
Selected
Subgrade
Base
Subbase
Selected
Subgrade
Base
Subbase
Selected
Sub grade
Base
Subbase
Selected
Subgrade
Base
Subbase
Selected
Subgrade
Effective elastic moduli (MPa) determined from
MOD* RSD**
235
220
130
85
205
230
100
55
390
1 180
210
200
150
230
125
85
195
220
120
55
240
145
58
220
210
151
23
210
200
155
37
270
400
499
210
230
150
163
43
194
* MOD measured depth deflections and RSD surface deflections
** Ratio of RSD!MOD
effective elastic moduli
Modular ratio**
1,03
0,42
1,00
1,15
1,00
0,71
0,34
2,28
1,02
0,66
0,45
2,59
1,02
0,66
0,23
3,82
1,03
0,71
0,31
4,91
For that reason the modular ratio of the base layer is constantly in the region of 1 in Table 5.1.
In the precracked phase of the cemented subbase, the effective elastic moduli determined from RSD measurements indicate a lower value than the one determined from MDD measurements.
In the cracked phase of the subbase, the modular ratio increases from the initial low 0,42 to a rather constant 0,6 to 0,7.
This still indicates an undercalculation with the RSD measurements.
The same tendency of undercalculation by using RSD measurements is also true when the effective elastic moduli of the selected layer are inspected.
In this case though, the undercalculation becomes worse with the increase in actual repetitions.
The subgrade, in contrast, is however constantly overcalculated when the effective elastic moduli determined with RSD measurements are compared with those determined with MDD measurements.
This overcalculation increases with the increase in actual repetitions.
It is therefore obvious from the calculated subgrade effective elastic moduli that the nonlinearity of the subgrade is not initially influencing the effective elastic moduli of the subgrade, but at a later stage of trafficking it seems to become more influential.
The shift in balance, when the subbase cracks, seems to have an effect on both the subbase and the selected layer underneath.
This shift in balance can also be reflected by the effective elastic moduli of the subgrade.
In Table 5.2 the effective elastic moduli as calculated from RSD deflection measurements are shown for a typical lightstructured granular pavement at Malmesbury (Horak, 1986a).
In this case no effective elastic moduli were determined with
MDD deflections.
It is clear though that the pavement balance did change to a much deeper structure as the actual repetitions increased.
The base and selected layers showed a steady decrease in effective elastic moduli as actual repetitions increased.
The structurally stronger subbase and the subgrade
showed initial decreases in effective elastic moduli.
but increased again towards the end.
The effective elastic moduli of the base and surfacing were again fixed at values as determined with the aid of other material information.
Actual repetitions
10
50 000
200 000
350 000
496 000
591 000
Layer description
Base
Subbase
Selected
Subgrade
Base
Subbase
Selected
Subgrade
Base
Subbase
Selected
Subgrade
Base
Subbase
Selected
Subgrade
Base
Subbase
Selected
Sub grade
Base
Subbase
Selected
Subgrade
Effective elastic moduli from
RSD deflections (MPa)
50
100
28
157
45
123
30
230
45
107
28
285
40
143
30
521
80
200
60
230
60
138
35
161
The procedure as set out in Section 3.3 was followed in a few selected cases.
This was done to determine whether the subgrades do exhibit nonlinear behaviour and whether it affects the calculated effective elastic moduli of the other structural layers.
The results are shown in Table 5.3.
In the case of the Erasmia test it is clear at the start of the test that there is no strong evidence of nonlinearity of the subgrade in depth of the pavement.
The average subgrade effective elastic modulus of 350 MPa is higher than the 230 MPa of the linear approach.
That difference is due to the calculation procedure of the nonlinear approach further away from the centre of loading.
It also illustrates some stress dependency as the calculation point is deeper into the structure in the nonlinear approach.
In the recalculation with BSFT of the effective elastic moduli of the other structural layers, the subbase did increase to a more realistic figure for a cemented subbase.
TABLE 5.3  Effective elastic moduli with a linear and nonlinear approach
Actual repetitions
Layer description
Effective elastic moduli (MPa)
Base
Subbase
Selected
Subgrade
Subgrade
Subgrade
Subgrade
Subgrade
Base
Subbase
Selected
Subgrade
Subgrade
Subgrade
Subgrade
Subgrade
Base
Subbase
Selected
Subgrade
Subgrade
Subgrade
Subgrade
Subgrade
400
499
210
_ 230
200
155
37
270
40
143
30
521
40
177
25
760
1 004
1 003
1 002
1 001
400
912
210
359
349
353
353
353
200
155
19
466
627
638
640
648
Towards the end of the test at Erasmia (1 009 000 actual repetitions) stronger evidence of nonlinearity was shown by the subgrade.
This tendency of nonlinearity is true in depth of the subgrade too.
In the recalculation with BSFT the selected layer showed a tendency to lower also as for the linear case.
It is believed that the structural strength of the selected layers is not reflected correctly.
Although there is evidence of stresssoftening behaviour this layer is forged into balance with the rest of the pavement structure.
This means that the subgrade underneath does not suddenly increase to a value of 466
MPa as a discrete event.
It is rather a gradual change from the value of 466 MPa to a lower value. but not necessarily as low as
19 MPa. when moving up towards the subbase.
In the case of the test at Malmesbury there is also definite indications of nonlinearity of the subgrade.
The effect on the other structural layers when recalculation with BSFT is done. is however minimal.
(a) Effective elastic moduli are calculated very effectively using the Multidepth Def1ectometer (MOD) measurements.
The effective elastic moduli calculated in this manner have been correlated very effectively with the mechanistic analysis procedure.
The procedure to calculate effective surface deflections was described linearelastic computer program.
(c) Effective elastic moduli of the various pavement layers in the stiff behaviour state are correlating well when values determined from surface deflection basin measurements are compared with those determined from depth deflections (MOD).
(d) In the flexible behaviour states the effective elastic moduli of the 5ubgrade, as determined from surface deflections, are determined 2 to
5 times larger than with the MOD deflections.
(e) The BSFT backanalysis procedure needs considerable assistance in the calculation of particularly the upper layers, in order to ensure unique results.
(f) The selected layer in a four or fivelayer pavement system is constantly under calculated compared to the upper layers, in order to ensure unique results.
(g) Nonlinearity of the subgrade can be modelled by the BSFT backanalysis procedure.
Nonlinearity does feature more strongly in the subgrade effective elastic moduli when the pavement is in the very flexible behaviour state.
This is probably due to the stresssoftening behaviour accompanying the normal change in balance towards a deeper pavement structure.
(h) The number of pavement structures that were backanalysed with the aid of the BSFT procedure are limited and results can be used only as mere indicators.
RELATIONSHIPS BETWEEN DISTRESS
DETERMINANTS
AND DEFLECTION BASIN
PARAMETERS : A LITERATURE SURVEY
6.1
CBA.PTER 6 : CONTENTS
Page
6.2
6.2
6. 11
Material characterization is greatly enhanced by the use of deflection basin measurements.
This has been described in the preceding chapters. This forms the basis of detailed analyses with multilayer linear elastic computer models in order to calculate typical distress determinants.
These distress determinants must normally reflect the two distress states, fatigue and rutting of the pavement.
In the analysis of flexible pavements the distress determinant for rut is vertical subgrade strain and for fatigue the distress determinant is that of the maximum horizontal asphalt strain. Jordaan (1986) defines the analysis approach outlined above as the nonsimplified approach.
It is possible to make use of empiricaltheoretical relationships between these distress determinants and deflection basin parameters.
Jordaan (1986) classifies the latter approach as a design curve approach. These relationships between the distress determinants and deflection basin parameters are precalculated or established by empirical relationships.
In the discussion in this chapter such relationships between deflection basin parameters and the distress determinants are highlighted as found in literature. A brief discussion on the validity of the use of these distres determinants are given too.
Fatigue cracking is a major type of distress in bituminous pavements.
The three basic types of cracking are: longitudinal, transverse and alligator or crocodile cracking.
Longitudinal cracking is mainly due to environmental effects.
Transverse and crocodile cracking are usually due to the effect of traffic loading.
Shrinkage cracking (transverse) is mostly kerbed by proper material specification and construction control.
The traditional distress parameter relating to the fatigue life of the asphalt layer is described by Snaith et ale (1980) as follows:
where:
N
= number of applications to failure
€HA = tensile strain repeatedly applied c. m
= material coefficients.
Normally researchers use the radial or horizontal strain (€HA) at the bottom of the asphalt concrete layer as the criterion.
This is also used for the mechanistic design procedure in South Africa.
Freeme et ale (1982a) however. refer to recent research indicating that the maximum tensile strain does not necessarily occur at the bottom of the asphalt layer.
Under certain conditions of low stiffness in the asphalt layer.
the principle tensile strain at depths 0.8
to 1 times the radius of the load area exceeds the magni tude of the strain at the bottom of the layer.
Typ ical relationships determined for horizontal strain (€HA) are shown for thin and thick asphalt layers in Figures 6.1 and 6.2 for typical
South African asphalt mixes.
Shift factors are used to compensate for the crack growth until the cracking is clearly visible.
For the South African condition these shift factors range from 2 to
10.
Although the maximum horizontal strain is normally calculated at the bottom of the asphalt concrete layer. as described above.
the effect of the thickness of this layer is also noted by researchers.
Anderson (1977) shows that asphalt concrete layers of 25 to
75 rom reached maximum tensile strain values at thicknesses of 50 to 75 rom for various pavement types as shown in Figure 6.3. Dehlen
(1962a) also noted that theory indicates that there may be a critical thickness of surfacing. in the range of 50 to 100 rom. for which flexural stresses are a maximum.
This same tendency is illustrated by Grant and Walker (1972) for various combinations of pavement structural strength and radius of curvature (R) (See
Figure 6.4). They also note: "For the majority of pavements where the asphalt thickness was less than 50 rom the maximum tensile strain in the asphalt layer was at the surface. while invariably being at the bottom of the layer for greater thicknesses." Freeme et a1, (1982a) and Patterson (1985) indicate that for such thin asphalt surfacing layers the total number of axles.
irrespective
lLl
J
(J)
Z lLl
Iz
<X a:
I
(J)
1000
800
'"
:i..
600
400
200
.......• i"'oo
..•....
•••••
......,;; ..•....
...•.•.
~
••••••
••...
""
I I I II
I
I III
I
I
I
AIR VOIDS 1,5  20·/ •
CONFIDENCE LEVEL 50%
,
~
I I I
I
I
I
TI
I
I
I
T'
STIFFNESS
(GPo)
AT 2O·C
""
"'24
'" 5' .•••••...
~
"'"
8~
~
"'"
"'"
"'"
"""
'" r'"
,
~"'"
"'"
~
'"
""""~
::::~
~
10
4
10~ 10
6
TRAFFIC (NO. OF AXLES)
(EQUIVALENCY COEFFICIENT n ~
1)
10
7
(J) z lLl
It:
<X a:
I
(J) lLl
J
'"
:i..
1000
800
600
400
200
~~~
","'
•...
......:
~
,"
STIFFNESS 'RANGEI 4,510
G'p6
AT
20·C, CONFIDENCE LEVEL 50 %
~
~ ~
"
~2
AIR VOIDS %
::l •••••
9 ~~
.•..
""
~
~~
•...
~
~
~~
.....
~
....
100
10
2
10
3
10
4
10~ 10
6
TRAFFIC (NO. OF AXLES)
10
7
(EQUIVALENCY COEFFICIENT n=
1)
(b) CONTINUOUSLY GRADED ASPHALTS
FIGURE 6.1
RECOMMENDED FATIGUE CRITERIA FOR THIN
BITUMEN SURFACINGS
(f)
Z
W
Iw
O
TRAFFIC
CLASS
"'EO
E4
El E2 E3
1000
<t ct::
W
00 z<t
=>0
...J
III
::l...J
w
ZW
J:
<t~ ct::
Iz
(f).x
500
100
50

r



10.
r.
~
~
10.
r

 
~~
::::
"""
"""

r.
r
~

•....

•....
.•..
.•..
.•..
.•..
•••• 10
STIFFNESS ( MPa)
i
__ oo l
.
0
3000
5000
8000
••
"'" 
..
....

.






~
..
10
10
5
10
6
EQUIVALENT TRAFFIC, E80
FIGURE 6.2
RECOMMENDED FATIGUE CRITERIA FOR THICK BITUMEN
BASES

en
c
0
'
Q) en c: fI)
<t c
'c
0
U

Q)
c:
Q)
.r::::.
Q.

0 c
.......
)(
~
E
::3
E
~
)( c
0
I
~

5
4
3
2
I
0
Pavements with weak bases
Pavements with strong bases
2
3
4 5 6 7
Asphalt layer thick ne
55
(in ches )
8
9
FIGURE 6.3
RELATIONSHIP BETWEEN A.C. THICKNESS AND
TENSILE STRAIN (Anderson, 1977)
140 
4  4 760 I 2 e
B
0
..
J
<l
:r:
Q.
(f)
<l
Z
5

<l
0::
..
(f)
W
J
(f)
Z
..
J
2 z
0
N
0::
0
:r:
10
4
104
0:(\1
~ E
105 mz z~
0
r
Iv w
D..
lO
" t:
V w:J
0:.....1
:J
106~
Q
<to o:~
11
(I) •..•.•
27,5 u.<t
10
7 ~ om z<t if
32
41
ASPHALT THICKNESS
150 mm
410MN/m
2
100 200
RADIUS OF CURVATURE (METERS)
FIGURE 6.4
CHART FOR DESIGNING AGAINST EXCESSIVE TENSILE STRAIN
IN
THE ASPHALTlr,rnnt nnrl Wnlkp.r_IQ7?)
.
6.8
of load. should be considered.
Molenaar (1983) refers to various researchers in order to make practical conclusions on cracking behaviour (for example cracking from bottom to top or vice versa).
and. in keeping with the recent research trend. also refers to fracture mechanics principles.
Various researchers have done extensive analyses on different pavement structures in order to arrive at regression functions of the deflection basin parameter and the distress determinant for fatigue cracking.
The typical relationships between asphalt tensile strain (€RA) and surface curvature index (SGI) for three subgrade conditions are shown in Figure 6.5 . This is true for typical threelayered pavements.
Anderson (1977) ana lysed the typical pavement structures in the
State of Victoria.
Australia.
in order to arrive at a delationship between surface curvature index (SGI). as defined by him versus the asphalt tensile strain (€RA) as shown in Figure 6.6.
All these pavement structures have asphalt concrete layers of 50 mm or less.
In this figure values are recorded for strains up to
2x104 (inch/inch).
Anderson (1977) concludes that this function can be used to estima~e asphalt tensile strains in an overlay design method.
In general these relationships have been determined for a granular based. threelayered pavement structure.
Monismith and Markevich (1983) expanded this work by analysing 300 different cases of this typical pavement structure.
Their resulting relationship was: where:
€t
DoD12
= maximum tensile strain
=
curvature function or surface curvature index (SGI) (see Table 1.1)
In essence.
this is also what was done by Grant and Walker (1972) as shown in Figure 6.4.
In this case. though.
a specific threelayered pavement structure was analysed (granular base) and the radius of curvature (R) was correlated with strain (€RA).
.....
..J
<J:
10
3
~
::>
~
X
<J:
~
U>
<J:
..J
•..
•....
~
ZZ
_0:::
0::: •....
oU>
I
5
10
SUBGRADE
MODULUS
(MPo)
10·
102
SURFACE CURVATURE
103
INDEX (SCI
)(/Lm)
FIGURE 6.5
RELATIONS BETWEEN SURFACE CURVATURE INDEX AND HORIZONTAL
ASPHALT STRAIN OR VERTICAL SUBGRADE STRAIN. (Molenaar, 1983)
50
100
150
>
\II z
3
10
<J:
•....
U>
W
0
<J:
0:::
C> m
::>
4
U>
10
..J
<J: u
.....
0::: w
>
SUBGRADE
MODULUS
(MPo)
10
1
102 103
SURFACE CURVATURE INDEX (SCI
)(/Lm)
.
0\
1.0
~

I
0
c:
)(
"'"
0 en c:
~
"'" c:
•...
+
en
+
1.8
1.6
1.4
1.2
1.0
0f/)
«
0.8
Curve (B)
=
Curve (A)
+
1.3
x S.D.
•


•
.
Deviation
=
O. 22 x 10
4

I"
_ I"A.C.
III
I" A.C.
FIGURE 6.6
SURFACE CURVATURE INDEX vs ASPHALT TENSILE STRAIN
(Anderson
I
1977 )
Kilareski, et al 1982) conclude from their analysis that the deflection basin parameters surface curvature index (SCI) and the base damage index (BDI) give better defined relationships with eRA than the parameter base curvature index (BCI).
The function of surface curvature index (SCI) versus maximum asphalt strain (eRA)' as shown in Figure 6.7, is the preferred relationship.
In this
Figure it is also indicated that the relationship is not linear, but at low strain levels a linear relationship may be used.
Permanent deformation of the individual layers resulting in permanent deformation of the total pavement structure is a major distress state to be considered in overlay design.
The nature and classification of rutting in asphalt concrete pavements are discussed in Appendix B.
As mentioned there, the distress determinant most often used is vertical subgrade strain
(e ) .
vs
As was noted this approach is more historical in the sense that it does not focus on the prevention of deformation, but on the results thereof.
The emphasis in this section is on the analysis and prevention of rutting.
The basic relationship used as a first approach is thus restated as follows:
N
= k(l
)n
e
vs where
N k, n
e
vs
= number of applications to failure
= material coefficients
= vertical subgrade strain as determined by, for example multilayer linear elastic computer materials.
Various researchers have analysed different pavement structures to arrive at regression functions of
e
vs parameters.
and the deflection basin
Such typical relationships are shown in Figure 6.8.
Anderson (1977) established a relationship between maximum deflection (dO) and vertical subgrade strain
(e).
vs
This is shown in
100
10
I
0 c:
0
•..

en
Q)
III c:
Q) l

11/
>C
0
~
E
::l
E
40
80
60
20
o o
FIGURE 6.7
RELATIONSHIP BETWEEN MAXIMUM TENSILE
STRAIN AND SURFACE CURVATURE INDEX.
( K i I a re ski, eta I ., 1982)
l40 4 4760/ 25 BD z z z
<i ~
"
~ b
5,0
(/)
:::
>
IU
>
(J)
1LI
(/) 0
1LI
<X
0::
0::
Q..
(!)
I,D
o m
::> u
(J)
0,5
...J
IJ..
0
~ Q..
0:: •...•
~ ti
0
10 I 000
10,000
REPETITIONS OF STRAIN
100 000
FIGURE 6.8
COMPARISON OF SUBGRADE STRAIN CRITERIA
( I in.
=
2,54 em (Yoder and Witzak
1
1975)
Figure 6.9
with two possible curves fitting the results of granular based three layered pavements ana lysed .
Monismi th and
Markevich (1983) also used 00 as the deflection basin parameter in their analysis of similar pavement structures.
That relationship where:
00 is measured in inches
E s
= subgrade modulus expressed in psi.
A high correlation coefficient was established.
for the pavement structures analysed.
allowing confidence in this method of estimating vertical subgrade strain (e: ) for this type of pavement vs
In the light of what was discussed in chapter 4 it is clear that maximum deflection (00) is not necessarily the most ideal deflection basin parameter to correlate with vertical subgrade strain (e: ) • vs
Wang et al.
(1978) established a relationship incorporating maximum deflection (° 0) and base damage index BCI for measurements with the Road Rater Model 400.
This is shown in
Figure 6.10.
On the use of vertical subgrade strain (e: ) as the distress vs determinant.
Molenaar (1983) notes: "Although these simple subgrade strain criteria are very easy to use and therefore very attractive, they are nevertheless thought to cover only a part of the permanent deformation of the pavement structure because each layer can exhibit some permanent deformation itself".
In Figure
6.5 it was shown how he relates subgrade strain to surface curvature index (SCI) as he did for maximum asphalt strain.
This should be kept in mind, since Grant and Curtayne (1982) also indicated that owing to densification of some layers the pavement is often structurally stronger at the time of overlay analysis.
This has been repeatedly confirmed by HVS tests.
r
40  4  4 760 I 31
'lit
I o
)( 8
~
Ol
.Q
o
~
Q)
0 c

(J)
6
~ 4
o o

~
~ 2
Curve (A) E =0.02370
 0
2
+
23.30
(Standard Dev.= 1.08xI0
4)
3
'Design' Curve (B).= (A)
+
1.3 x S.D.
.020
.030
Deflection (inches)
FIGURE 6.9
DEFLECTION vs SUBGRADE STRAIN (Anderson, 1977)
ROAD RATER MODEL 400
FREQUENCY  25 Hz
H
U m
I.L
o o
10
3 toe:( a::
I 10
ROAD RATER MAXIMUM DEFLECTION
8 max
(I03cm)
FIGURE 6.10
RELATIONSH I P BETWEEN BASE
CURVATURE INDEX, MAXIMUM
DEFLECTION AND SUBGRADE
COMPRESSIVE STRAIN
( Wan 9 ) eta I ., I
978 )
In an effort to assess the accumulated permanent deformation in all the pavement layers, Treybig et a1.
(1978) calculate the following stresses and strains:
(a) vertical strain at the bottom of the top layer
(b) vertical stress at the bottom of the top layer
(c) vertical stress at the bottom of the second layer
(d) horizontal stress, parallel to the load axle, at the bottom of the second layer
(e) vertical stress at the bottom of the third layer
(f) vertical strain at the bottom of the fourth layer
(g) vertical stress at the top of the fifth layer
(h) vertical strain at the top of the fifth subgrade layer.
These stresses and strains are the largest values, irrespective of their horizontal position under the loaded wheels.
The values are correlated to the number of repetitions (N).
These correlated functions are derived from the analysis of pavement structures' bound and unbound bases.
The deformation in the bitumen or asphalt concrete layer was referred to in Appendix B.
The Shell method of estimating deformation in this layer, as described by Van de Loo
(1976) is well established.
Work by Viljoen and Meadows
(1981) on the creep test provides practical guidelines for South African conditions on the prevention of permanent deformation in the asphalt concrete layer.
In conclusion it may be stated that the maximum tensile strain in the asphalt layer
(8
HA) is the distress determinant that is most associated with fatigue cracking due to the ease of calculation.
Various research efforts have been reported that characterize and explain the actual cracking behaviour.
It is concluded that, in the South African mechanistic design procedure, the method currently used to determine maximum tensile strain (E HA) at the bottom of the asphalt layer is acceptable.
Regression analyses relating
E
HA to the desired deflection basin parameters indicate that this is an acceptable method to be used in overlay design.
The majority of analyses though, were done for a basic granularbased threelayered pavement structure.
In the light of the previously proposed pavement categories and the behaviour states, (see chapter 4), similar analyses should be done in order to establish possible relationships, for example on bitumenbased and cementtreated base pavements.
This will be possible with the available information from the recorded HVS tests and other field observations.
The interactions of cementtreated layers and cracks reflected through the upper layers and asphalt concrete layers are well recorded and should also be analysed in this way as they are the cause of cracking in a high percentage of pavements in South Africa.
It can be stated that vertical subgrade strain (E vs
) is the distress determinant most often calculated in order to predict rutting.
This is the practice in South Africa and multilayer linear elastic computer programs are usually used to calculate
E vs
Various deflection basin parameters have been related to
E vs by regression analysis in order to estimate
E directly from vs deflection basin measurements.
A clear distinction is not always made in regard to the pavement type analysed, although the typical threelayered granular base pavement prevails.
As was suggested in the previous section, analyses should be done with the available South African data in order to classify or do regression analyses for each of the aforementioned pavement classes or behaviour states.
From this discussion, HVS tests results and field results it is clear that all the layers contribute to the total permanent deformation.
Various other distress determinants are calculated by methods incorporating the stress and strain states in the various layers.
It is suggested that on this line, regression
analysis be done too.
various pavement categories.
This in turn should be related to the
RELATIONSHIPS BE'l"WEEN DEFLECTION BASIN PARAMETERS
AND DISTRESS DETERMINANTS FOR TYPICAL SOUTH AFRICAN
PAVEKENTS
3 DEFLECTION BASIN PARAMETERS VERSUS DISTRESS DETERMINANTS
3.1
General
3.2
Vertical subgrade strain
3.3
Maximum asphalt strain
4.
RELATIONSHIPS WITH OTHER STRUCTURAL PARAMETERS
4.1
General
4.2
Granular base pavements
4.3
Bitumen base pavements
4.4
Subgrade elastic modulus
5 THE EFFECT OF OVERLAYS
5.1
Granular base pavements
5.2
Bitumen base pavements
7.7
7.7
7.7
7. 1 1
7.16
7.16
7.16
7.20
7.22
7.23
7.23
In the analysis of flexible pavements for rehabilitation design the mechanistic rehabilitation design procedure can be used with confidence (Freeme, 1983 and Freeme et aI, 1982).
It has been explained in chapter 4 how proper material characterization is an important step in this analysis procedure. The normal linear elastic computer programmes are used in such an analysis in order to calculate the distress determinants and relate them to structural life. In chapter 4 and Appendix C and D it was explained how this nonsimplified or fundamental approach ( Jordaan, 1986) should function.
In the previous chapter it was shown how it is possible to develop design curves for specific pavement types whereby deflection basin parameters are related to distress determinants. In this chapter it will be shown how this author analysed typical South African flexible pavements in order to relate selected pavement deflection basin parameters to the distress derminants. The broad spectrum of flexible pavements is properly defined and the analysis is further restricted to bitumen, granular and cemented base pavements.
The latter type is analysed in the equivalent granular state which means that their analysis is similar to that of the granular base pavements.
They have a further common factor in the asphalt surfacing (40 mm average or less).
In the discussion reference is also made to the findings of overseas researchers.
Overlaying flexible pavements is an important rehabilitation alternative.
For that reason the effect of various overlay thicknesses were also investigated in relation to the effect on the deflection basin parameters.
The pavement structures in the Catalogue of designs (NITRR, 1985a) reflect the typical pavement structures used in South Africa.
The pavement types can be subdivided into pavements having granular, bituminous, cemented and concrete bases.
Typical granular base
pavement structures analysed, are shown in Figure 7.1.
Only the subbase, base and surfacing layers are shown; the selected layer and subgrade are excluded.
The latter two layers are, however, prepared in the standard prescribed way (NITRR, 1985a) and are common to all these pavement structures.
The different pavement types behave differently.
Their behaviour is timedependent; generally pavements become more flexible with time.
This necessitates the proper definition of the current state of the pavement in order to determine the most appropriate analysis or design method of predicting future behaviour.
The definition of the states of pavement behaviour is given by Freeme (1983); these states range from very stiff to very flexible (See chapter 3 and
4).
A flexible pavement is defined as a pavement structure of which the behaviour is controlled by material in the granular state.
In chapter 3 it was shown how the various deflection basin parameters can enhance such accurate definition of behaviour state.
The analysis of flexible pavements therefore includes granular, bitumen and cemented base pavements.
Pavements with cemented bases or subbases were considered to be in the cracked phase, exhibiting equivalent granular behaviour (Freeme, 1983). All such standard TRH4
(NITRR, 1985a) flexible pavements were analysed first by means of the multilayered linear elastic program, MECD3 (Maree and Freeme,
1981a).
A second level of analysis was done on granular base pavements or bases in the eqUivalent granular state with the computer program ELSYM5 (University of California, 1972). The ELSYM 5 program (University of California, 1972) tends to be inaccurate in calculating surface deflections between 100 mm and 250 mm from the point of maximum deflection.
This is true for bituminous base pavements (Tam, 1985).
This tendency is more pronounced when fivelayered pavement structures are analysed and when the pavement structure is more rigid, for example a concrete base pavement
(Taute, McCullough and Hudson, 1981).
For that reason the detailed
.
analysis of the bituminous base pavements were done with the BISAR program (Horak, 1985).
I rO  4  ~I06 II 80
ROAD
CATEGORY
EO
<0.2 X 10
6
GRANULAR BASES
E1
0,20,8 X 10
6
E2
0,83 X 10
6
E3
312 X 10
6
E4
1250 X 10
6
50 At
15061
VV
;st
V 12562 V 15062
"
!?~
15065 .
/
/
// 150C4
30A t
OR Sf
12561
40A f
15061 t
~1~OOG4
'/ 100C4
~v st
/V 12562
;V st
V 15062
// 150C4 ..'
/ ~.O~
..
'0
.
f
SYMBOL A DENOTES AG, AC OR AS.
SYMBOL S DENOTES S2 OR S4
FIGURE 7.1
Typical granular base pavements from the Catalogue of deslgns
Catalogue of designs (NITRR, 1985a), surface deflections were calculated at various offsets perpendicular to the axle of the wheels.
The structural integrity of a pavement is reflected in varying degrees of accuracy by various deflection basin parameters.
The deflection basin parameters that were investigated in this study are listed in Table 1.1 (for ease of reference use the fold out at the
back).
The formulae and measuring devices normally associated with them are also listed (Horak, 1984).
The deflection parameters vary from the traditional singular point, maximum deflection, to deflection basin parameters such as spreadability and area, which are highly descriptive of the deflection basin as a whole.
In the
ELSYM5 analysis of the granular base pavements, deflection basin pavements calculated in this region carried less weight in the analysis.
In all of these analyses the wheel load used was a 40 kN dual wheel load with a standard tyre pressure of 520 kPa.
A Poisson ratio of
0,44 was assumed for bituminous materials and 0,35 for all other types of material.
The elastic moduli values of the materials used in the MECD3 analysis were the average values as defined and verified with HVS test results (Freeme et al., 1982a and Freeme,
1983).
The value for thin asphalt surfacings (mostly granular base pavements) was set at 2 000 MPa.
The selected subgrade's elastic modulus was set at 120 MPa and the subgrade modulus was varied with
50,70 and 150 MPa.
In the ELSYM5 analysis of granular base pavements (and equivalent granular states) the base elastic modulus and thickness were identified as the most influential structural components in terms of the deflection basin parameters (Tam, 1985).
These values were varied over a range commonly found in practice (Freeme, 1983).
The base thicknesses were varied in steps of 25 mm between 100 and 250 mm.
The effective elastic modulus of the granular base was varied in steps of 15 MPa between 100 and 450 MPa.
Also, in order to determine the effect of overlays on granular base pavements, the surfacing thickness was increased in steps of 10 mm (up to 100mm thick) over a basic surfacing thickness of either 20 mm or 40 mm.
In the detail analysis (Horak, 1985) of bitumen base pavements the
BISAR computer program was used.
In Table 7.1 the various structural components are listed.
Overlay elastic modulus (MPa)
Overlay thickness (mm)
Surfacing elastic modulus (MPa)
Surfacing thickness (mm)
Base elastic modulus (MPa)
Base thickness (mm)
Subbase elastic modulus (MPa)
Subbase thickness (mm)
Selected subgrade modulus (MPa)
Selected subgrade thickness (mm)
Subgrade elastic modulus (MPa)
3 000*
5, 10, 40, 60
2 000, 4 000
10, 40
3 000, 5 000, 7 000
80, 150, 220
150, 500
300*
120*
150*
50, 70, 150
*
These values were typical representative values and their variance has a minor influence (Tam, 1985) on deflection basins.
The deflection basin parameters listed in Table 1.1 (see the fold out for ease of reference) were calculated for each flexible pavement structure in these analyses.
As pointed out in the introduction the intention is to determine which parameters can be related to the typical distress determinants (€HA and €vS) accurately.
Only those deflection basin parameters that have a clear and meaningful relationship with the distress determinants are reported here.
The calculated vertical subgrade strain (€VS) was correlated with the various deflection basin parameters of bitumen bases and granular bases separately. This relationship is not possible for flexibile pavements in general.
The reason for this is shown in
Figure 7.2.
Both base types show a relationship between SCI and
€VS and discern the variance in subgrade elastic modulus.
As in the relationships between equivalent layer thickness (H ) and SCI e
(see Appendix F), there is a difference in gradient between the relationships for bitumen and granular base pavements.
Additionally, in the case of the granular base pavements these relationships shown in Figure 7.2, are only valid for average values of elastic moduli and layer thickness of the base.
In
Figure 7.3
the relationship between BDI and €VS for granular bases, shows that no discernment is made between subgrade elastic moduli being varied.
This is however also true only for average values of base elastic moduli and layer thicknesses.
In Figure
7.4 the relationships between R, F1, Q and SD versus €vS are shown for bitumen base pavements.
It seems that these relationships are not influenced by the variance in the structural input values, as granular base pavements seem to show a tendency for. Of all these ralationships shown in Figure 7.4 the deflection basin parameter
SD has the most significant relationship.
BITUMEN BASE

GRANULAR BASE
~ 1000
<t a::
Ien
I
:::l..
\V en 500
>
100
10
l/
"
~
Es = 50MPa ~
~
/' ,/
~s= 70 MPa l/
l/"""
/
/
/
./
V
,
/
I
E = 15~MPa
/
.".
Es= 50MPa
.
/
I
,
.J'rf'
!/
./
.•
'/
~ ~
./
./
",
/'
,
/
,
,
~ ~
I'
"
/ j
IE s' = 150 ty1Po_
"
~
/"
I·
/
,/
""
I
SURFACE CURVATURE INDEX (SCI)
100
(fLmH r: 305 mm)
Surface curvature
FIGURE 7.2
index versus vertical subgrade strain
GRANULAR BASE
..•.
z
<r a::: l
(/)
1000
\1/ en
>
500
Es=50,70,150 MPa
I
V
I
/
,
J
"
II
/
/
/
~
100
10
100
'BASE DAMAGE INDEX (B DI)(fLm)
FIGURE 7.3
BASE DAMAGE INDEX VERSUS VERTICAL SUBGRADE
STRAIN
500
Z
<f a::
I
(f)
I
:l
200
100
III
In
>
50
20
10
0,1
E s = 50 MPo
Es= 70 MPo
Es= 150 MPo
Es = 50 MPo
Es=70MPo
Es = 150 MPo
10
100 200 500 1000 2000
RADIUS OF CURVATURE (R)
500
Z
« a::
I
(f)
I
:l
100
III
In
50
>
500
200
100
50
Es = 50 MPo
Es = 70 MPo
Es = 150 MPo
~
10
10 20 50 100 200 500
SLOPE OF DEFLECTION (SOl
10
0,1
0,2 0,5
DEFLECTION RATIO
(Q)
FIGURE 7.4
BITUMEN BASE DEFLECTION BASIN PARAMETERS VERSUS
VERTICAL SUBGRADESTRAIN
The calculated maximum asphalt strains, (€RA' at the bottom of the base) of typical bitumen base pavements were related to the various deflection basin parameters separately.
In Figure 7.5 it can be seen that a typical value such as 5CI (r
=
500 mm) correlated well with €RA' but, as Molenaar and Van Gurp (1980) indicated, there is no clear discernment between the various subgrade elastic moduli.
In Figure 7.6, deflection basin parameters 5, A, F1 and BCI proved to be better in that respect by discerning the variance in subgrade elastic modulus.
In this figure the relationship with BCI is the most significant and usefull.
When the maximum asphalt strains (€RA' under the surfacing) of bitumen base pavements were related to deflection basin parameters, clear, simple relationships became limited to those as shown in Figure 7.7.
Area (A) and spreadability (5) can discern the effect of variance in subgrade elastic modulus, but both seem to be rather insensitive to changes in their respective values.
As the €RA values are compressive, the significance for fatigue calculation of the surfacing is further nullified.
The thickness of the asphalt surfacing layer of a typical granular base pavement has a marked effect on the calculated value of the maximum asphalt strain (€RA).
Grant and Walker (1972) showed that for threelayered pavement structures there is a sharp increase in maximum asphalt strain (€RA) values when surfacing thickness is increased to 25 mm . Thereafter the strain increased slowly to reach a maximum strain value between surfaces with 40 and 100 mm thickness.
In Figure 7.8 this effect is verified when radius of curvature (R) is correlated with €RA for various thicknesses of the surfacing.
The subgrade elastic modulus was kept at a standard 70 MPa, but the base elastic modulus and thickness were varied for the granular base pavements.
For bitumen base pavements the subgrade elastic modulus was varied though.
Figure
7.8
clearly shows that for a normal granular base there is a defini te difference in the relationships between R and ERA for various thicknesses of asphalt surfacing.
At a thickness of 80 mm and above, such a pavement is according to definition (Freeme et
",
~ v
/
,
,
,
~
'"
I
Es = 50, ~O, 150
, I
I I
I
I
I I IIII
BITUMEN BASES
I
rPa
10
10 \00
SURFACE CURVATURE INDEX (SCIHj.Lm> (r
500
=
500 mm)
FIGURE 7.5
Surf ace curvature index versus max i mum asphalt strain for bituminous base pavement structures
~ 500 c:r a:: l
(J)
I
~
UJ
(J) c:r
CD lJ..
0
~
~
I
0
CD
III
'<
100
10
BITUMEN BASE
Es
50 MPa
70 MPa
150 MPa
100
S PR EADABI LI TY
(S l
500
(J)
Z500
« a::
I
I
.5
UJ
(J) c:r
CD lJ..
0
~
~
b
CD
~
III cr
:z:
100
10
Es
50 MPa
70 MPa
150 MPa
100
AREA (Al
500
Z500
<i a::
I
(J)
~
~
UJ
(J) ca 
100 lJ..
o
~
b
CD
III cr
J:
_
10
~
Es =70MPa
100
SHAPE FACTOR (F
1) (X
10
2)
500
500
Z
<i a::
I
(J)
UJ
~ 100
CD
~
~
~
b
CD
Es=l50 MPa
Es= 70 MPa
E s =
50 MPa
100 500
BASE CURVATURE INDEX (BCr>~m)
FIGURE 7.6
BITUMEN BASE DEFLECTION BASIN PARAMETERS VERSUS
MAXIMUM ASPHALT STRAIN UNDER THE BASE
500
(J)
Z
<r
tt::
I
~
E
..

I
Q)
>
0u; en
~ a:::
::::l
(J)
~
C) z u
<l:
J:
III
200
100
80
50
20
10
10
BITUMEN BASE
AREA (A)
E s
SPREADABILITY (S)
FIGURE 7.7
MAXIMUM ASPHALT STRAIN UNDER SURFACING
VERSUS AREA AND SPREADABILITY
CIl
Z

<t
0::
I

1000
:i:
:::>
:i:
X
<t
:i:
~
<t
J:
Cl.
CIl
«
Z
«
0::
I
..J
«
Iz
0
N
CIl
I
::1..

c(
0:: :t:
0
III
J:
100
10
10
GRANULAR BASES
BITUMEN BASES
MPa
100 1000
RADIUS OF CURVATURE (R){m)
10000
FIGURE 7.8
RADIUS OF CURVATURE VERSUS MAXIMUM ASPHALT STRAIN
al., 1982a) and (NITRR, 1985a) rather classified as a bitumen base pavement.
Proof of the latter is that this relationship (80 mm and 100 mm surfacing) extrapolates to the relationship established for bitumen base pavements.
In Figure 7.9
it can be seen that other deflection basin parameters such as S, SCI, F1 and Q tend to group surfacing thicknesses of 40 mm to 100 mm together, while those with thicknesses of up to 20 mm is apart.
This reaffirms the observation by Grant and Walker (1972) discussed earlier.
Of these relationships that with SCI can be termed the most significant.
It is clear from the results of the previous section, that it is not always possible to form clear, simple relationships between distress determinants and deflection basin parameters.
The reason for this seems to be the conflicting influences that other structural input parameters being varied, have on the calculated distress determinants.
This is more pronounced in the case of the granular base pavements than with bitumen base pavements.
The literature survey in the previous chapter and chapter 4 already indicated there are peculiarities with the linear elastic layered programmes used (in the vicinity of the loaded wheel).
In the case of granular bases in particular the variance of elastic modulus of the base and asphalt surfacing thickness had a significant effect on the calculated deflection basin parameters.
The effect of the variance of the elastic modulus of the granular base is best illustrated in Figure 7.10 where SCI, BCI,
Q and R are related to the base elastic modulus.
Surfacing thickness
(HSF) is however not being discerned by parameters BCI and
Q.
A very useful relationship was developed between maximum horizontal asphalt strain (€HA) and easily measurable parameters
z
<i a::
I
.
(J)
I
:l
100
40100 mm
SURFACING
THICKNESS
20mm
GRANULAR BASES
E s : 70 M Po z ex a::
I
(J)
I
5
100
4O100mm
SURFACING
THICKNESS
Z
<t a::
I
CI! 100
:l
100
SPREADABILITY (S)
500
40100mm
SURFACING
20mm
THICKNESS z ex a::
I
(J)
I
:l
100
100 500
SURFACE CURVATURE INDEX (CSt>
( fLm)
40100 mm
SURFACING
THICKNESS
100
SHAPE FACTOR
(Fj) (
X
16
2)
500
100
DEFLECTION RATIO
(Q)( x
10
2)
500
FIGURE 7.9
GRANULAR BASE DEFLECTION BASIN PARAMETERS VERSUS
MAXIMUM ASPHALT STRAIN
GRANULAR BASES
E
=
70 MPc o
100 a.
:E
CXl
W
50
20
ASPHALT
SURFACING ..
THICKNESS
(mm)
100 80
10
10 20 50 100 200
SURFACE CURVATURE INDEX
(S C I
)(fL
m )( r = 305 mm)
500
d:
100
:E
50
CXl
IJJ
ASPHALT SURFACING
THICKNESS (mm)
10
10 20 50 100 200
RADIUS OF CURVATURE(R) (m)
500 o a.
100
:E
10
0, I 0,2 0,5 I 2
DEFLECTION RATIO (Q)(r=305mm)
5
10
10 20 50 100 200 500
BASE CURVATURE INDEX (BC!)(,u.m)
FIG U R E 7.10
GRANULAR BASE ELASTIC MODULUS VERSUS DEFLECTION
BASIN PARAMETERS
for granular regression.
base pavements, by means of
The relationship is as follows:
ERA
=
1360,03 F1 + 4,54 HSF 2,10 R+3806,29
Q
2563,82 where: ERA
= maximum asphalt strain (~strain)
F1
= shape factor
HSF
= asphalt surfacing thickness (mm)
R
= radius of curvature (m)
This relationship has a Rsquare value of 92,4 per cent and a coefficient of variability of 9,7 per cent.
Maree et al.
(1982a) have shown that for granular base pavements.
permanent deformation originates mostly within the base itself.
In order to limit or indicate the potential for permanent deformation in a granular layer, Maree (1978) suggested the use of a safety factor, f
= k{ 3 tan
2(
45 where
a1; a3
C
=
Apparent cohesion o
= angle of internal friction
= major and minor principle stresses
K
= constant, depending on the mois.ture condition.
The safety factor will therefore vary depending on the typical shear parameters (C and
0) and the moisture condition.
Typical shear parameter values and moisture conditions (wet or dry) as suggested by Freeme (1983) were used to calculate safety factors for the wet condition (F wet) and for the dry condition (F dry).
These calculations were done for typical granular base material (G1 to G4).
Additionally the deviator stress (ad) for each situation was calculated too.
The safety factors (F wet and F dry) and the deviator stress
(ad) were correlated with the calculated deflection base parameters by means of a stepwise multiple regression analysis.
The number of variables in the final equation was limited to three or the Rsquared value had to exceed 0,75.
The results of these regression analysis are shown in Table
7.2.
The deflection basin parameters that correlated the best with
F wet and F dry, were the shape factor F2 and the index parameter BCI.
The deviator stress ad correlated very well with the surfacing thickness and the index parameter BCL
The other deflection basin parameters that occurred in the relationships were; Fl, Q610' sD, BDI and s.
(See Table 1.1
for definitions.)
The significance of these relationships are that for a granular base type, the potential for permanent deformation can be determined by calculating either F wet, F dry or ad from deflection basin parameters.
The same type of relationship was developed for bitumen base pavements by means of a stepwise multiple regression analysis.
The relationship before overlay is as follows:
MATER IAL
CODE
Gt
G2
G3
G4
GI TO G3
DEPENDENT
VARIABLE
F
WET
F
ORY
O"d
F
WET
F
ORY
O"d
F
WET
F
ORY
O"d
F
WET
F
ORY
O"d
F
WET
F
ORY
O"d
REGRESSION
FUNCTION
 5 ,80
+
15,84 (·F2) 45,25 (BCI) + 4,85 x 10
3
(HSF)
8,07+ 28,06 (F2) 116,30 (BCI) +9,56 x 10
3
(HSFl
240,731,93(Hs.J+3704,43( F1l197,51 (BCI)
10,04
+
3,77 (Fil19,OI (0610l  4,00 (F, l
 6,03+ 13,74 (F.'2l
+
2,48 (BCIl55,79 (SO l
.
72,58 2,40 (HSFl + 6848,40 (BCIl

3,68 + 6,23 (F2)
7,41 + 12,67 (F2l
43,38 2,55 (HSF) + 6329,04 (BCI)
0,14 + 21,19 (BoI)  3,08 (°610)
2,46 + 8,09
(F2 )  4,50
(°610 )
1,182,45 (HSFl+5447,25 (BCIl
 0,971  0,048 (S l + 38,96 ( BoI l + 9,76
X
10'! (F2l
1,78 +2,25 x102 (Fzl+66,31 (BoIlO,07(Sl
85,09 + 12703,27 ( BCIl4003,98 (Barl.I, 16 (F2l
ELASTIC MODULUS OF SUBGRADE
=
70 MPa
DEFLECTION BASIN PARAMETERS AS DEFINED IN TABLE 1.1
R
2
0,77
0,80
0,95
0,80
0,81
0,95
0,77
0,78
0,97
0,77
0,77
0,84
0,77
0,78
0,81
10g10 €
RA
:= 0,996
(10g10 SCI)  0,352 (10g10 S)
(10g10
Q)
+ 2,521 where: €RA := maximum (tensile) asphalt strain (~strain)
This relationship has an Rsquare value of 0,99 and a coefficient of variability of 16,5 per cent.
When this relationship is determined for bitumen bases with overlays it looks as follows:
10g10 €RA
= 
0,623 (10g10 A)  0,619 (10g10 Q)
 0,365 (10g10 SCI)
+ 3,470
This relationship has an Rsquare value of 0,61 and a coefficient of variability of 80,1 per cent.
The effect of the overlay is such that this relationship with only three independent variables reduces the Rsquare value considerably and increases the coefficient of variability to unacceptable limits and the use thereof is not recommended.
A relationship between deflection at 2 m and subgrade elastic modulus was derived similar to that derived by Molenaar and
Van Gurp (1980).
In this cas'e though, it is applicable to all types of flexible pavements with four or five layers.
This relationship is:
7.23
log E s where:
=
9.727  0.989 log 62000
E s
62000
=
subgrade elastic modulus (Pa)
=
deflection at a distance of 2 m from the centre of loading
(1JlI1).
This relationship is shown in Figure 7.11 where the subgrade moduli had been correlated with deflections at 500. 610 and
915 mm.
too.
It is obvious that the gradient of the relationships change from deflection at 500 mm (6500) to deflection at 915 mm (6915), but from the latter deflection up to deflection at 2 000 mm (62 000) the gradient of the relationships stays virtually the same.
It is the general feeling (Tam.
1985) that deflections nearer than 500 mm
(6500) to the centre of loading. would increasingly reflect the influence of the other structural layers. nearer to the surface ( base and subbase).
Granular base pavements in the dry regions of South Africa have typical surfacing thicknesses of 30 to 50 mm (40 mm average) thick.
Alternatively surface treatments typically have thicknesses of 20 mm for double surface treatments.
As shown in Appendix F.
these thin asphalt surfacings have relatively little influence on the value of equivalent layer thickness (H ) and therefore also on vertical subgrade strain e
(€vS)' as the thickness of the overlay is increased.
In the wetter regions of South Africa thicker asphalt surfacings and overlays may be applicable.
The effect of overlay thickness on €VS is illustrated; in
Figure 7.12.
The greater the overlay thickness. the more €VS is reduced.
An elastic modulus of 3000 MPa was assumed typical for the asphalt overlay and an elastic modulus of
z o
100
I
U
Lu
...J
I.L.
IJ.l
o
50
10
10
20
SUB GRADE
50
MODULUS
100
(MPa)
200
FIGURE 7.11
SUBGRADE ELASTIC MODULUS VERSUS DEFLECTION
z
<[ a:
I
<fl
550
500
>
:5
450 a:
IJJ
OVERLAY
THICKNESS
(mml
EASPHALT=3000 MPa
ESUBGRADE = 70 MPa
Eys=VERTICAL
SUBGRADE
STRAIN a: 400
IJJ
I
U.
<[
\U
en
>
350
300
400 450 500 550 600 650
EyS BEFORE OVERLAY (,uSTRAINI
FIGURE 7.12
Effect of overlay thickness on su bgrade strain of granular base pavements
70 MPa for the subgrade layer.
Overlay thicknesses of 60 mm or more would substantially reduce
€ • but asphalt layers of vs such total thickness (surfacin~ plus overlay) are classified as bitumen base pavements (Freeme et al..
1982a).
Such overlay thickness would therefore rarely be applicable.
Possibly as levelling courses to correct excessive rut irregularities.
In the discussion of the selection of overlay thicknesses. it is assumed that granular base pavements have either an existing surface treatment with maximum thickness of 20 mm or a premix asphalt surfacing layer with a typical thickness of
40 mm.
This original asphalt surfacing thickness has a deciding influence on the deflection basin in the vicinity of the wheel load.
This is best reflected in Figure 7.13 which shows surface curvature index (SCI) values before and after overlays of various thicknesses.
It can be seen that for granular base pavements with a maximum original surfacing thickness of 20 mm.
an overlay of at least 40 mm will be needed to reduce SCI values.
For a granular base pavement with an original surfacing thickness of 40 mm.
a 20 mm overlay will lead to a reduction in SCI values.
This means that there is a reduction in SCI values. only after a total thickness of 60 mm.
The influence of the original asphalt thickness is even more pronounced when the effect of overlays of various thicknesses on the reduction in maximum horizontal asphalt strain (€HA) is considered.
In Figure 7.14 the values of €HA before and after overlays are shown for original surfacing thicknesses of both 20 mm and 40 mm and for various overlay thicknesses.
For a granular base pavement with an original surfacing thickness of 20 mm. an overlay of over 80 mm would clearly be needed to reduce €HA values. and this is seen as impractical and costly.
A granular base pavement with an original asphalt thickness of 40 mm may only require an overlay of
20 mm to reduce €HA if the value of €HA before overlay was more than 250 ~strain.
.•.
;)
)
,.
I
')
I
) t_
ESURF : 3000 M Po
ES: 70 MPo
>
<:
~ 150 w o a:: w llL.
<:
100
OVERLAY
THICKNESS (mm)
H
U
<n
50
40mm SURFACING
BEFORE OVERLAY

o
100
SCI(~m)
20 mm SURFACI NG
BEFORE OVERLAY
150 200
BEFORE OVERLAY
(r=305mm)
250
FIGURE 7.13
EFFECT OF OVERLAY THICKNESS ON SCI.
(r =305 mm) OF GRANULAR BASE PAVEMENTS
_ 500 z
<t
Q:; f
(/)400
I
::t
ASPHALT
SURFACING
MAX. 20 mm
BEFORE
OVERLAY
>
<t
..J
Q:;
IJJ
> o
300
80mm/
~
~,
~
Q:;200
IJJ f
~
<t
ASPHALT SURFACING
40 mm BEFORE
OVERLAY
\lJ
~':'IOO o o
EASPHALT'=
3000
MPa ;EHA =MAXIMUM
ASPHALT
ESUBGRADE = 70 MPa STRAIN
100  200 300  400
EHA BEFORE OVERLAY
<1'
STRAIN)
FIGURE
7.14
Effect of overlay thickness on maximum asphalt strain of granular base pavements
Overlay thicknesses have the same effect on bitumen base pavements as on granular base pavements in general, concerning the effect of reducing subgrade strain (€vS)' In
Figure 7.15 it can be seen that the thicker the overlay, the more the reduction in €VS'
The subgrade, as varied in terms of elastic moduli, also has an influence in terms of a difference in gradient for the thicker overlays (40 and 60 mm). Each subgrade condition has a definite range over which they are applicable too.
For the overlay of 10 mm, subgrade moduli variance does not have an influence.
This thickness would normally not be considered for such a purpose.
Deflection basin parameters calculated before and after an overlay reflect a change with various degrees of significance.
In Figure 7.16, deflection basin parameters, S, Fl,
SCI and SD clearly show the effect of overlay thicknesses on values before and after overlays.
In general Fl, SCI and SD show a reduction in values while S shows an increase in values when overlaid.
The indications are not the same though in terms of a structural improvement as SCI and SD are insensitive to changes in elastic moduli of the subgrade (50,
70 and 150 MPa).
The relationships determined for Sand Fl are true only for a subgrade modulus of 70 MPa.
Overlays reduce the asphalt strain under the base (€HA) as can be expected.
The thicker the over lay, the more the reduction.
In Figure 7.17 it is shown how this is true for bitumen base pavements of which the subgrade elastic moduli were varied from 50 to 150 MPa.
In the whole analysis it was assumed that no existing cracks occurred in the base, as this would definitely need a different analysis procedure.
z
I
3
400
>c:r
...I
a:: lJ.I
c:r a::
I
CJ) a::
300 w l
LL.
c:r
III
CIl
>,


OVERLAY
THICKNESS
10 mm
40mm
60 mm
EVS i"
VERTICAL
SUBGRADE
STRAIN
100
100 200
EVS
300 400
BEFORE OVERLAY CfJ  STRAI N)
500
FI GU RE 7.15
EFFECT OF OVERLAY THICKNESS ON SUBGRAOE
STRAIN FOR BITUMEN BASE PAVEMENTS
70
>c::r
...J
a::
UJ
>
0 a::
UJ
I
IJ..
c::r
en
60
50
BITUMEN
BASE
Es =70MPa
Esurf = 3000 MPa
OVERLAY
THICKNESS t
40mm
/
50 60
S BEFORE OVERLAY
7.31
a::
0,6
UJ
~ a::
UJ
I
IJ..
c::r
IJ..
0,8
BITUMEN BASE
Es
= 10 MPa
Esurf = 3000 MPa
10"m
,/
40mm
/
60mm t
OVERLAY
THICKNESS
0,2
0,4
0,6 0,8
F1 BEFORE OVERLAY g
~
~
I v
I o v m a::
200
UJ
>
~a::
UJ
I
IJ..
c::r
100
14
U
en
BITUMEN BASE
Es = 50,10,150 MPa
. Esurf = 3000 MPa
OVERLAY
THICKNESS
10~m
100 200 seI BEFORE OVERLAY
(x t0
2l(mm)
300
BITUMEN BASE
Es =50,10,150
Esurf = 3000 MPa
MPa a::
300 lLJ
~ a::
UJ
I
IJ..
c::r o
en
OVERLAY
THICKNESS
~
10mm
200/40mm
~60~
100
200
300 400
SO BEFORE OVERLAY
FIGURE 7.16
INFLUENCE OF OVERLAYS OF BITU/WEN BASES ON DEFLECTION
BASIN PARAMETERS
<t a:::
ILl
IlJ..
a:::
ILl
>
0
400
Z a a:::
I
en
•
::t..

~
..J
300
200
ILl
en
<t
CD a:::
ILl
0
Z
::::>
<l:
:r:
III
100
0
0
BITUMEN BASE
ESURFACING
ESUBGRADE
=
3000 MPo
=
50, 70, 150 MPo c
HA
=
MAXIMUM ASPHALT
STRAIN
60mm t
OVERLAY
THICKNESS
100 200 300 400 cHA
UNDER
BASE
I
BEFORE OVERLAY(fLSTRAINl
FIGURE 7.17
EFFECT OF OVERLAY THICKNESS ON MAXIMUM
ASPHALT TENSILE STRAIN OF BITUMEN BASE
PAVEMENTS
Some deflection basin parameters can be related to distress determinants
(E:
VS and
E:
HA) in meaningful and clear relationships.
In some cases though no discernment can be made with a variance in subgrade elastic moduli.
This is not a great concern as simple and clear relationships are still possible.
The simultaneous variance of other structural parameters such as surfacing thickness and base elastic modulus and thickness, lead to a lack of simple meaningful relationships for granular base pavements in particular.
The calculated value of surface curvature index (SCI) versus vertical subgrade strain (E:VS) is a useful relationship for granular and bitumen base pavements.
There is a clear discernment when subgrade elastic moduli are varied.
The gradients of the relationships also differentiate between the two base types (granular and bitumen).
Bitumen base pavements seem to be less influenced by the simultaneously varied structural input parameters referred to earlier.
Clear relationships between deflection basin parameters F1,
R, SD and'
Q versus vertical subgrade strain (E: VS) are examples.
The maximum asphalt strain (E:HA) calculated under the base of bitumen base pavements, correlates well with deflection basin parameters such as S,
A,
F1, and
BCl.
When maximum horizontal asphalt strain (E: HA) is calculated under the surfacing of such bitumen base pavements, the values are compressive which reduces its significance for fatigue calculation.
The effect of varying the subgrade elastic modulus was discerned by the abovementioned deflection basin parameters.
The thickness of surfacing of granular bases has a definite effect on relationships between deflection basin parameters and €HA. The difference in the effect of asphalt thickness is clearly illustrated in the relationships between radius of curvature (R) and maximum horizontal asphalt strain
(E:
HA) for granular and bitumen bases.
The tendency for
deflection basin parameters.
such as S. SCI. Fl and
Q.
to group together granular base surfacing thicknesses.
of 40 mm to 100 mm differing from the effect of thicknesses of up to
20 rom.
is in line with work previously done in this regard.
Overlays of flexible pavements reduce sub grade strain (£VS) increasingly as thicknesses of overlays increase.
This does not mean though that it is a viable and economic procedure to reduce subgrade strain (£VS).
For granular base pavements the overlay thicknesses required to reduce £VS is more than that normally applied in practice.
Such thick overlays could in some cases be applicable to levelling courses on granular base pavements in order to correct excessive rut irregularities.
Overlay thickness of granular bases does have an effect on the calculated values of deflection basin parameters.
Surface curvature index (SCI) values reflect a reduction when granular base pavements are overlaid.
The thickness of the original surfacing does have a major effect on SCI values.
Even better relationships were found for bitumen base pavements for S. Fl. SCI and SD.
It is even possible to show that SCI and SD reflect changes due to overlay thicknesses.
irrespective of subgrade elastic moduli.
The original thickness of a granular base surfacing influences the required thickness of overlay for a reduction in asphalt strain (£HA)' Thin original surfacing layers
(less than 20 rom) require impractical thick overlays (80 rom and more) to reduce (£HA)' Original surfacing thicknesses of
40 rom require overlays as thin as 20 rom to reduce £HA' The base thickness of bitumen bases (more than 80 rom) is sufficient to require normal practice overlay thicknesses to reduce asphalt strain (£HA)' Overlay thicknesses as low as
10 rom reduce £HA at the underside of the base.
Such thin overlays are however also impractical.
PROPOSED USE OF DEFLECTION BASIN HEASUREKENTSIN THE
!
MECHANISTIC ANALYSIS AND REHABILITATION OF FLEXIBLE PAVEMENTS
2.1
2.2
2.2.1
2.2.2
Deflection basin parameters
Equipment and measurement
Network level
Project level
3 ENHANCEMENT OF THE MECHANISTIC REHABILITATION DESIGN
PROCEDURE WITH DEFLECTION BASIN MEASUREMENTS
3.1
General
3.2
3.3
3.3.1
3.3.2
3.3.3
Identification of pavement behaviour states
Material characterization
General
Normal material characterization
Material characterization with deflection basin measurements
Backanalysis of effective elastic moduli
3.4
3.4.1
3.4.2
3.4.3
3.5
3.5.1
3.5.2
3.5.3
3.5.4
Analysis of flexible pavement structures
General
Rutting
Cracking
Rehabilitation design
General
Granular base pavements
Bitumen base pavements
Practical considerations
4.1
General
4.2
Measuring equipment
4.3
Material characterization
4.4
Analysis procedures
PAGE
8.2
8.2
8.4
8.4
8.5
8.13
8.13
8.13
8.16
8.17
8.17
8.17
8.20
8.21
8.21
8.22
8.22
8.23
8.6
8.6
8.7
8.9
8.9
8.9
8.12
In this chapter this author endeavours to summarise this study on deflection basin measurements by presenting it in a format that would enhance the present mechanistic rehabilitation design procedure. The discussion summarises the proposed measurement of deflection basins on a network and a project level. Deflection basin parameters that describes the full deflection basin. are suggested for general use.
It is shown how the selected deflection basin parameters can enhance the accurate description of the pavement behaviour states.
Better material characterization is facilitated by using the relationships established between material properties and deflection basin parameters.
In the analysis of typical flexible pavements the relationships between deflection basin parameters and distress determinants are discussed to show how such a design curve approach can enhance the nonsimplified approach. Although mention is made of rehabilitation design.
the reference only applies to the mechanistic rehabilitation design procedure.
Overlay design as an option is high lighted in this chapter.
Finally this author indicates what future research needs to be done on deflection basins.
In chapter 1 the deflection basin was discussed in great detail.
Various deflection basin parameters were defined as listed in Table
1.1.
In summary it can be stated that deflection basin parameters must:
(a) Represent the full range of characteristics of the whole deflection basin (not only maximum deflection.
but rather a combination of parameters covering the whole deflection basin)
(c) Be able to relate to the structural characteristics of the full depth of pavement structures.
In chapter 2 it was shown that irrespective of the measuring equipment the majority of these deflection basin parameters can be calculated fairly easily. It was shown that the full deflection basin as such does not have to be measured.
It was suggested that only deflections on the deflection basin be measured at selected offsets.
The offsets that are suggested are at 0, 127, 305, 610 and 915mm
(the offset at 127mm is seen as optional as it is only related to radius of curvature). As can be seen from Table 1.1 the majority of the deflection basin parameters can be calculated using the deflections measured at these points. In the discussion in chapter 3 it was shown that the deflection basin parameters that are the most significant in terms of their description of pavement behaviour state and material identification are the index parameters. They are ;
Surface curvature index ( SCI)
Base damage index (BDI)
Base curvature index (BCI).
These deflection basin parameters describe the deflection basin in full.
Surface curvature index (SCI) desribe the area of positive curvature in the immediate vicinity of the load (see Figure 2.7).
This reflects on the structural capacity of the base and surfacing' layer. Base damage index (BDI) describes the transitional zone of the deflection basin where the positive curvature changes over to that of the reverse curvature.
This reflects on the structural capacity of the base and subbase layers. Base curvature index (BCI) describes the area of the reverse curvature.
This reflects strongly on the structural capacity of the lower layers such as the selected layer or subgrade.
Other deflection basin parameters that can be used as assistance in the analysis procedure is that of slope of deflection (SD) or m~ximum deflection or radius of curvature (R). The latter two are included purely to ensure the change over from the traditional deflection basin parameters and their related relationships with pavement
analysis can be used as an enhancement with the proposed index parameters.
The various measuring devices are discussed in detail in Chapter 1.
In general the ideal measuring device should:
(a) Realistically simulate moving traffic loads in terms of magnitude of load, shape and equivalent time of loading
(b) Accurately measure the whole deflection basin with high levels of reproducibility
(c) Be simple to operate, so that it could be used with confidence in the field, but it should also be applicable to research
(d) Be capable of attaining high levels of productivity, which must reduce the cost of testing.
The NITRR Deflectograph (previously the Lacroix deflectograph) is used on a network basis in South Africa by the road authorities, with a proven level of efficiency.
It is believed that this will still be the primary function of this measuring device.
In the discussion in chapter 1 it was shown that no other nondestructive measuring equipment can compete with this apparatus in terms of productivity and cost per measuring point.
With the old Lacroix deflectograph only the maximum deflection was used to distinguish between various uniform sections of road.
This author instigated the change with the new NITRR deflectograph whereby amongst others deflections are measured on the full deflection basin at the offsets as suggested in the preceding section. This means that the most significant deflection basin parameters can be calculated ( ego index parameters).
The IBM computer on board the NITRR deflectograph accumulates the data and from that level data manipulation becomes a standard procedure with other personal
computers in the data processing unit. The ease of the data manipulation of the NITRR deflectograph enables the engineer to give a more fundamental evaluation of the pavement condition even at the network level which previously was not possible.
This will be explained in more detail later in this chapter.
On a project level detailed assessment of a pavement section is required.
The requirements listed above narrows the list of
?ossible
nondestructive deflection basin measuring equipment down to only two. The falling weight deflectometer (FWD) seems to be the most appropriate device when measured against these prerequisites.
The FWD is a system which has proven its reliability in environments overseas.
The ease and speed of operation and transportability gives it the edge over the road surface deflectometer (RSD). It will take a considerable time before such an apparatus can be commisioned for general use in South Africa.
It is suggested that, should such a system become available in South
Africa, it be properly calibrated against the road surface deflectometer (RSD).
This should preferably be done on various pavement types and behaviour states.
Accelerated tests with the
Heavy Vehicle Simulator (HVS) would provide the ideal situation for such calibration.
The RSD. as used during accelerated tests under the HVS. is however, still the main reference device for nondestructive deflection measurements of pavements in South Africa.
The vast extent of the information recorded on various pavement types under various testing conditions.
behaviour states and material states.
makes it possible to do extensive modelling of pavement behaviour.
The deflection basins of the pavement, as measured with the
MultiDepthDeflectometer (MOD). are also available for further comparative studies on the same pavement structures and loading conditions.
The RSD measures the full deflection basin and therefore does not confine the analysis to specific deflection basin parameters.
The WASHO procedure of measuring.
as is used
under the HVS.
limits the effects of plastic deformation.
The wheel approaches the measuring point while the typical rebound procedure. as is still used with the standard Benkelman beam truck.
measures plastic deformation too.
The RSD can therefore be used with the same standard Benkelman beam truck. but with a different measuring procedure.
The setup for measuring the deflection basin with the RSD already exists. as used in combination with the Crack Activity Meter (CAM)
(see Appendix E).
The procedure of data management and analysis for the RSD is well established and is described in detail in chapters 2 and 3. The relationships developed during accelerated tests with the RSD will make it a powerful 1 tool in the hands of the engineer during the detailed assessment phase.
In the rest of the chapter this will be discussed in more detail.
3 ENHANCEMENT OF THE MECHANISTIC REHABILITATION DESIGN PROCEDURE WITH
DEFLECTION BASIN HEASUREHENTS
In chapter 4 and 6 reference are made to the mechanistic design procedure. The mechanistic rehabilitation design procedure as used in South Africa is well established and verified with the fleet of accelerated testing facilities. the Heavy Vehicle Simulators (HVSs)
(Freeme, et al., 1982b and Freeme, 1983).
However, where this rehabilitation design method is lacking, is in making better use of nondestructive measurements to make this rehabilitation and design process more effective.
Deflection basin measurements have been underutilized in South Africa as they were mostly limited to the use of maximum deflection and radius of curvature measurements.
This has resulted in empirical relationships which reflected little information on fundamental material and pavement type behaviour.
The use of deflection basin parameters in the rehabilitation and analysis of flexible pavements was investigated and the suggested
incorporation thereof in the existing mechanistic rehabilitation design procedure is described in the sections to follow.
The behaviour catalogue is an extension of the existing design method.
the TRH4 (NITRR.
1985a) which also has a catalogue of designs.
The basic philosophy followed in the catalogue of rehabilitation designs and that of the TRH4 (NITRR.
1985a) is therefore similar.
This is illustrated in the flow diagram of the mechanistic pavement rehabilitation design method in Figure 4.1.
For the reader's convenience this figure is repeated here as Figure
8.1.
The First step is always to identify the pavement class.
An in depth discussion of pavement class distinction or selection is given in TRH4 (NITRRa. 1985) and will not be repeated here.
The second phase illustrated in Figure 8.1 is to correctly identify the pavement type.
This identification is done in terms of the base layer type.
The base types are defined as: Granular.
bituminous. cemented or concrete.
This subdivision of pavements.
based on base types.
is clearly described by Freeme (1983) and
Freeme et al. (1986) in terms of the difference in the performance.
or behaviour of these basic pavement types and the resultant difference in the behaviour states and catalogue selection.
Deflection measurements are the basis of the definition of the pavement behaviour states.
Approximate ranges of maximum deflection (6 ) are used to subdivide the pavement behaviour types o into very stiff.
stiff.
flexible and very flexible behaviour states.
These ranges of maximum deflection (6 ) and an abbreviated o description of the general behaviour are shown in Table 3.1.
Deflection basin parameters that were measured on various pavement types during accelerated tests (see chapter 3) were used to give a better definition of the various pavement states.
These deflection basin parameter ranges are listed in Table 3.2
and repeated in
I.
PAVEMENT CLASS
A,
B,
C
2.
3.
PAVEMENT TYPE
GRANULAR BASE
BITUMINOUS BASE
CEMENTED BASE
CONCRETE
,
PAVEMENT STATE
VERY STIFF
STIFF
FLEXIBLE
VERY FLEXIBLE
.
6.
5.
4.
PAVEMENT LAYER STATE
WET, DRY,
,
CRACKED
DESIGN INPUTS
LAYER THICKNESS
ELASTIC MODULI
EVALUATION f
CATALOGUE OF BEHAVIOUR
STATES.
MECHANISTIC ANALYSIS
FIGURE 8.1
FLOW DIAGRAM OF THE MECHANISTIC
PAVEMENT REHABILITATION DESIGN
METHOD (FREEME, 1983)
Table 8.1
for the various pavement behaviour states.
It is suggested therefore that the index parameters rather than maximum deflection be used in the identification of the pavement behaviour state.
The pavement behaviour states of particular interest in this discussion are the flexible and very flexible behaviour states.
In general it will also mean that the pavement types as shown in
Figure 8.1 will be narrowed down to granular bases. bitumen bases and cemented bases.
As the latter type will mostly be in a cracked layer state.
the flexible cemented bases will be analyzed as a granular or equivalent granular base type.
For a correct analysis of a pavement in the mechanistic rehabilitation design procedure it is very important that the material of the various layers are identified correctly.
In
Figure 8.1 it is shown how the class. type. the behaviour state and state of the layer materials are used to characterize the pavement layer materials.
This normal approach can be enhanced by the incorporation of deflection basin parameters in the analysis procedure. but such deflection basin parameters can also be used to describe the pavement materials more directly.
The normal approach whereby material is characterized is where the principle input for the material properties (layer thickness.
effective elastic moduli and Poisson
I s ratio) is determined from basic pavement and material information.
This is best illustrated by referring to Figure B.1 (see Appendix B) where it is shown in the flow diagram that both destructive and nondestructive testing results are used to do effective material characterization.
This ties in with the approach outlined earlier for the mechanistic rehabilitation design procedure (Freeme.
1983).
Information from
TABLE 8.1 Behaviour states defined by deflection ba sin parameters
Behaviour state
~
Max. defl.
(mm)
Deflection basin parameter ranges
(x
SO
10
6)
SCI
(mm)
BDl
(mm)
BCl
(mm)
Very stiff
< 0,2
<
50 < 0,01 < 0,01 <0,01
Stiff 0,2  0,4
50400
0,01  0,2 0,01  0,1 0,01  0,05
,
0,40,6 400750 0,2 0,4
0, I  0,15 0,05  0,08
Flexible
Very flexible
>.0,6
>750 > 0,4 > 0,15
>
0,08
asbuilt information, condition surveys, traffic surveys and deflection surveys form the pool of information of the nondestructive testing.
Destructive testing like in situ Dynamic
Cone Penetrator (DCP) surveys or coring of cemented or treated materials for material sampling and laboratory testing, are normally done during a second phase detailed analysis.
Such information is very valuable as even standard laboratory tests can be used to characterize layer material into various material classes as specified in TRH14 (NITRR, 1985b) and abbreviated in
TRH4 (NITRR, 1985a).
Freeme et al. (1982a) and Freeme (1983) also give a detailed description of the various material classes.
The use of more sophisticated laboratory tests like triaxial tests, repeated loads triaxial tests, repeated loads indirect tensile tests, beam tests, creep tests, etc. can only enhance the correct description of materials.
The mechanistic design method in general encourages the use of  such sophisticated tests.
The effective elastic moduli relationships used in the design method are based on extensive tests of this kind to determine the basic material characteristics.
Freeme et al.
(1982a) and Freeme (1983) do provide transfer factors for the various pavement classes and pavement layers to relate such sophisticated laboratory results to actual behaviour as measured under accelerated testing. The DCP results enhances not only the proper material characterization,but with the balance curves concept ( de Beer, 1986) the analysis procedure.
Finally it is therefore possible to accurately determine the basic input parameters for the mechanistic analysis, if adequate knowledge and experience concerning such a characterization are available.
Freeme, et al. (1982) and Freeme (1983) give a detailed description of each material type, material states and possible configuration in a pavement structure.
The effective elastic moduli can therefore be read off such tabulated values.
It is believed that, as considerable time and engineering judgement have already gone into the correct material identification up to this stage, any uncertainty can be overcome by doing a sensitivity analysis on such pavement structures during the analysis phase.
The subgrade is an important layer in the analysis of a pavement.
The effect that this layer has on the general shape of the deflection basin was discussed in detail in chapter 4.
In chapter
7, it was shown that there exists a very good correlation between subgrade elastic modulus and deflection measured on the reverse curvature of the deflection basin.
These relationships are true for all flexible pavements with up to five structural layers.
These relationships are as shown in Figure 7.11.
It is suggested that more than one deflection be used in the determination of the subgrade elastic modulus and an average value can be determined.
A further refinement can also be added by only using deflection values greater than 0,01 mm to avoid problems with measurement inaccuracies.
The elastic modulus of the base of a granular base pavement can also be determined from Figure 7.10 if the subgrade modulus is 70
MPa.
As shown in this figure, various deflection basin parameters can be used to determine the subgrade elastic modulus.
The effect of the surfacing thickness is also taken into consideration.
Although the subgrade effective elastic modulus is not varied. this figure can be used to determine a first approach to the base elastic modulus value in analyses.
The effective elastic moduli as determined with depth deflections from Multidepthdeflectometer (MDD) measurements, are the reference values as determined under accelerated testing.
These effective elastic moduli were used extensively to verify the tables of effective elastic moduli as proposed by Freeme (1983) and Freeme et al. (l982a).
In Chapter 5.
it was described and illustrated how surface deflection basin measurements can be used to backcalculate effective elastic moduli.
The linear elastic computer program
BISAR was used to backcalculate effective elastic moduli.
The
basic procedure is to use deflections on the outer edge of the deflection basin to calculate the effective elastic modulus of the lowest layer (subgrade).
Hereafter deflections nearer to the point of loading are used to calculate the effective elastic modulus of the next layer nearer to the surface.
By thus each time using deflections nearer to the point of loading. the effective elastic moduli of layers increasingly nearer to the surface are calculated.
Although the backanalysis procedure as outlined above can be defined as a standard procedure.
considerable manual interference is still needed to arrive at unique layer effective elastic moduli.
In conclusion.
it can be stated that the confidence in the indirect material classification, as outlined earlier, rates the necessity for such direct approach backcalculation procedure as a confirmative bonus.
In Figure 8.1
it can be seen that once the material characterization, also called design inputs, is completed, the last phase, namely the evaluation, can be tackled. As shown in Figure
8.1 the catalogue of behaviour states can be used in the analysis.
as described by Freeme (1983). The nonsimplified approach
(Jordaan.
1986) on the other hand is still the standard procedure where the linear elastic computer programmes are used to calculate the various distress determinants.
This approach is also described in great detail by Freeme (1983) and will not be repeated here. The deflection basin parameters can however be used in a design curve approach (Jordaan, 1986) whereby the selected deflection basin parameters are related to the various distress parameters.
This approach was investigated in detail in chapter 7.
The main distress determinants relating to rutting and fatigue cracking are discussed here in the analysis proses.
Vertical subgrade strain
(€ ) is directly correlated to various vs deflection basin parameters as described in chapter 7.
Only the preferred deflection basin parameters outlined earlier, are used here, but the relationships described elsewhere for these parameters can also be used.
The vertical subgrade strain
(€ ) was correlated with the various vs deflection basin parameters for the basic pavement types, bitumen and granular bases, separately.
In Figure 7.2 Surface Curvature
Index (SCI) is shown versus vertical subgrade strain
(€ ) for vs granular and bitumen base pavements.
In the case of granular bases a relationship between base damage index (BDI) and subgrade vertical strain
(€ ) can be used without regard to the sub grade vs effective elastic moduli.
This relationship is.shown
in Figure
7.3.
In the mechanistic rehabilitation design procedure deformation or rutting is kerbed by the limitation of vertical subgrade strain
(€ vs
).
In Figure 8.2 these fatigue life criteria as verified by accelerated testing are shown.
The various pavement classes are differentiated as shown.
By first determining the vertical subgrade strain with the deflection basin parameters ,the remaining life can be determined as outlined in Appendix C.
Although deformation of the whole pavement structure cannot be assessed, the mechanistic rehabilitation design procedure as described by Freeme (1983) does allow for indirect design.
In the case of granular bases the calculation of safety factors~ based on the basic shear parameters (C and 0) and the moisture condition of the pavement layers, limit deformation in such a granular layer by set criteria (Maree et al., 1982).
Freeme (1983) expanded these criteria for the equivalent granular states of cracked cemented layers and thus limiting deformation in the cemented layers, too.
If the quality of the granular base material is known, the safety factor can be determined using the regression functions as determined in Table 7.2 for that specific subgrade condition.
The fatigue life criteria as discussed by Freeme (1983) can then be used to determine the remaining life of such a granular base layer.
DESIGN TRAFFIC CLASS EO EI
en
>
III
104
..J
<t
U
....
0::: lLl
>
LaJ
0
<t
0:::
C)
CD
~
en
Z
<t
....
en
10
3
10
2
10
~ LIGHTLY TRAFFICKED
ROADS (C)
I
I
II
Iii
I
I
EMAJOR ROADS (S)
~
 FREEWAYS (A)
E2
104 10
5
10
6
EQUIVALENT TRAFFIC, ESO
E3
E4
FIGURE 8.2
Recommended vertical subgrade strain criteria for different road categories
Deformation in the bituminous layers are also limited indirectly in mechanistic analysis and rehabilitation design procedures.
Thompson et al. (1986) indicate that rut development in such layers are controlled by the proper selection of materials.
mix design. and construction control.
Freeme et al. (1982a) clearly indicated how this same approach was followed and verified with accelerated testing.
Additional criteria developed to kerb creep (Viljoen and
Meadows.
1981) indicate the continued development in this direction.
The critical parameter most commonly used to predict or govern fatigue cracking of bituminous layers.
is the maximum horizontal asphalt strain
(eRA) at the bottom of the layer.
In chapter 6 it was indicated that cognizance is given to the fact that the maximum asphalt strain does not always occur at the bottom of the asphalt layer. but that the criteria as used in the mechanistic rehabilitation design procedure does lead to satisfactory results in the majority of cases.
In Figure 7.8 radius of curvature (R) is related directly to maximum horizontal asphalt strain
(eRA).
This is true for bitumen base pavements without regard to the subgrade support condition.
For the granular base pavements the relationships shown are true only for the effective elastic modulus of 70kN.
The surfacing thickness of granular base pavements has a definite influence on the relationship between maximum horizontal asphalt strain
(eRA) and other deflection basin parameters.
Other deflection basin parameters.
like surface curvature index (SeI), is less sensitive to various surfacing thicknesses, but still sensitive to discern between thin
«
20 mm) and thicker (4) to 100 mm) surfacings.
These relationships are shown in Figure 7.9 for a subgrade effective elastic modulus of 70 MPa.
A combination of deflection basin parameters and basic layer thickness information can also be used to determine maximum
horizontal asphalt strain (€HA) by means of the regression relationships developed in chapter 7.
Design curves and relationships as discussed above can therefore be used to determine maximum horizontal asphalt strain values for bitumen bases or asphalt surfacings of granular bases.
The mechanistic rehabilitation design procedure is unique in the sense that fatigue relationships were developed for thin asphalt layers
«
50 mm) and for thick bituminous base layers (> 80 mm).
These relationships are shown in Figures 8.3 and 8.4.
In the case of thin asphalt layers, not equivalent 80kN axles (E80 's), but actual axle repetitions independent of loading are considered.
Remaining life can then be determined as outlined in Appendix D.
The South African mechanistic rehabilitation design procedure
(Freeme, 1983) is ideally suited for rehabilitation design.
The general tendancy would be to determine which distress determinant of which layer does not make the reqUired structural design life.
Remedial measures are then applied to lengthen the structural life of such a pavement under consideration. This may constitute various options of which overlays are but one option . As the discussion in this chapter is geared towards the distress criteria, maximum asphalt strain and vertical subgrade strain, overlay design will also be the focus of the deflection basin related rehabilitation design.
Deflection basin parameters were used to determine these distress determinants.
Overlays of various thicknesses were analyzed for the typical pavement types, granular and bitumen base pavements, in the flexible behaviour state.
The results as
1000
800
1&1
::I..
....•
600 z
«
400 a:
I
en
LIJ
...J
200
(f)
Z
LIJ
I
.......•
~ i"'lo..
..•.....
I"'"
~
......•
~
.......•
I I I II .1
I
I I}
I
AIR VOIDS 1,5  20%
I I
II
CONFIDENCE LEVEL 50%
I I I.
,,~ lo..
r"
:::::
"
"'"
II
'.
• I I'
STIFFNESS (GPo) AT 20°
2,4
5
Ill ••••
8~
~
...•.
!'~
,
.....
~
.•...
....
" t".
~ ~
......•
"
~
.....
""""
r': .....
•••••
10
4
10~ 10
6
TRAFFIC (NO. OF AXLES)
(EQUIVALENCY COEFFICIENT n
=
1)
10
7
00
00
1&1
::I.. 6
00 z
«
4 a: li;
00
LIJ
...J
en
2 z
LIJ
I
00
~~~
"'" ..•..•
......:
"""
..•..
1"" ••••
STIFFNESS RANGEl 4;51'0
~
~~IRVOIDS%
~,
~~
I'o~
~ ~
GP'~
AT
20°C, CONFIDENCE LEVEL 50 % ~
~

.
100
10
2
10
3
10
4
105 10
6
TRAFFIC (NO. OF AXLES)
(EQUIVALENCY COEFFICIENT n= 1 )
10
7
~
~ ~~
~~
~
.•...
(b) Continuously graded asphalts
FIGURE 8.3
Recommended fatigue criteria for thin bitumen surfacings
IJ.JO
...J¢
en
z
IJ.J
I
DESIGN
TRAFFIC
CLASS
'EO
EI E2 E3 E4
«
0:::
IJJ
00 z«
~O
...J
III
::L...J
IJ.J
ZIJ.J
_I
«~
0:::
Iz
en.¥
1000
500
50
100





"""'
"'r
~

~
""'"'
"""
•..
~
"""


I"'r:::r:::






...
...
...


...

STIFFNESS (MPa)
:t
000 ••
....::: 2 000 ••
__ 3000 ••
5000
8000
,....

"'1
r
r...


...
..
l""~
"'1
10
10
5
10
6
EQUIVALENT TRAFFIC ,ESO
(Use equivalency coefficient
10
7 n=4)
FIGURE 8.4
RECOMMENDED FATIGUE LIFE CRITERIA FOR THICK
BITUMEN BASES
Granular base pavements in the larger dry regions of South Africa have surfacing thicknesses in the order of 30 to 50 rom.
Thin overlay surfacings (20 rom) cannot be expected to have a significant influence on the reduction of subgrade strain.
In Figure 7.12 it is shown that for a subgrade effective elastic modulus of 70 MPa an overlay thickness of 60 rom and more would substantially reduce subgrade strain.
but asphalt layers of such total thicknesses are classified as bitumen base pavements.
Overlays of such thicknesses would therefore seldom be applied to granular base pavements except in the wetter regions of South Africa.
EXisting asphalt surfacings were classified as surface treatments
(20 rom and less) or normal thickness surfacings (40 rom average) for overlay purposes to curb fatigue cracking.
The effect of this original surface thickness is clearly shown in Figure 7.13
where various thicknesses of over lays (20.
40.
60 and even 80 rom) are shown related to the predefined existing surfacing thicknesses.
The normal practice with existing surface treatments requiring an overlay is to ignore the thickness of asphalt surface treatment.
equate it to the granular base and apply another surface treatment.
In normal practice a pavement with an original thickness of 40 rom.
however.
can recieve an overlay of any required thickness in order to reduce the calculated strain values.
Subgrade strain (t ) can be reduced by overlaying.
In Figure 7.15
vs it is shown that knowledge on the effective elastic moduli of the subgrade is a prerequisite as the variance in subgrade effective elastic moduli lead to different gradients for the various overlay thickness relationships.
As overlay thicknesses are increased.
maximum asphalt strain calculated under the base is reduced.
In Figure 7.16
it can be seen that this reduction in maximum asphalt strain.
by means of overlaying.
is true even if the effective elastic modulus of the subgrade is varied as indicated.
In the design and selection of overlays of flexible pavements, the standard practice should also be considered.
Granular base pavements with a double surface treatment (20 mm) would normally receive another surface treatment of about 20 mm.
Granular bases with surfacing thicknesses of 30 to 50 mm, can also receive a surface treatment.
Overlays of 30 to 40 mm are more typical in the dry regions of South Africa, while thicker overlays may be considered in the wetter regions of South Africa.
As soon as it has been established which of the distress determinants, namely maximum asphalt strain or subgrade strain, would determine the overlay thickness, the situation with the overlay should be checked with the remaining distress determinant.
This situation is of particular importance for granular base pavements where a total asphalt surfacing of 40 to 80 mm, in order to curb deformation, may in fact reduce fatigue life drastically
(Freeme, et al., 1982a).
This author sees this thesis only as an exploratory excercise on deflection basin measurement and use in the mechanistic rehabilitation design procedure.
There is an awareness that in a sense more questions are now asked than answers given to the initial questions asked at the outset of this study. The author nevertheless endeavoured to steer his investigation along the path whereby the new information gained on deflection basins and their use in analysis procedures can be of practical use. For that reason the well proven
South African rehabilitation design procedure was used as a main reference in the discussions throughout.
This approach also led to the identification of a number of areas in this field that urgently need further attention in future research efforts.
The author therefore attempts to identify these needs and motivate the research in the various areas separately.
The RSD as being used in South Africa was specifically developed for the HVS testing system. This apparatus is a natural extent ion of the
Benkelman beam.' This is in effect also the problem with this apparatus in the sense that, just like with the standard Benkelman beam, a truck is needed to do the measurements with the equipment and at least 3 persons to operate it. A need for equipment like the FWD which bridges these problems is therefore obvious with the advantages as listed elsewhere in this thesis. As mentioned elsewhere in this thesis, this type of equipment however needs to be properly calibrated and compared to the RSD. The accelerated testing with the
HVS provides the unique opporunity to do just that.
The new NITRR deflectograph can measure the deflection at suggested offsets.
This makes this equipment a more effective tool of evaluation on the network level. Considerable work still need to be done in order to relate such measured deflection basin parameters to the specific material and road conditions.
The relationship between
RSD deflection basins and that of the deflectograph needs proper investigation in order to enable the transfer of relationships developed for the former to be used with the latter.
The limited investigation of measured deflection basins with the RSD during accelerated tests enhanced the mechanistic rehabilitation design procedure by enabling more accurate identification of pavement behaviour states. Seen at the back ground of the vast extent of similar information on measured deflection basins being available
,the need for an in depth study in this field is glaringly obvious. A larger sample would facilitate the possibility of establishing relationships between deflection basin parameters and specific layer materials in specific behaviour states and for specific pavement types to that of the distress determinants.
This semiempirical approach can greatly enhance the current mechanistic rehabilitation design procedure.
The possibility of backcalculating effective elastic moduli from RSD measured deflection basins is an area that need considerable attention.
The procedure as outlined in this thesis, making use of linear elastic computer programmes can be developed much further in spite of the obvious short comings.
The possible use of finite element programmes or elastoplastic computer programmes like the
VESYS programwarrents a closer look. The possiblity of establishing regression relationships between deflection basin parameters as measured with the RSD and MOD may be an avenue to explore too. The effective elastic moduli as calculated with the help of MOD measured deflections are still considered as the most reliable values.
The possibility of establishing relationships between deflection basin parameters and other parameters of other design methods should also be investigated.
A typical possible relationship could be between the area (A) parameter and the DSNSOO number of the
DCPmodel.
The analysis of the standard pavement structures being used in South
Africa can be expanded considerably to include other typical pavement types and behaviour states.
The most influential parameters were identified in the initial analysis, but the small size of the analysis limited the application of the design curves that were established to very specific conditions.
It is also believed that other distress determinants relating to fatigue cracking and deformation need to be considered in such an analysis.
The possibility of using the emperical theoretical relationships established between deflection basin parameters and distress determinants were explored.
The limited relationships established however has consideralble constraints in their application.
This confirms the need for a much broader analysis of various pavement types to be analysed as expressed in the previous section.
These design curves can then be incorporated in a computer programme which automatically relates the measured deflection basin parameters to these relationships and calculate the life of a pavement type or the rehabilitation design.
Various mathematical and physical models available, and tested using the prepared RSD data sets.
were selected
The discussion of these models are divided into two subgroups namely; Linear and nonlinear models, based on the procedures of regression analysis used.
In both cases the SPSS Statistical Package for the Social
Sciences (Nie et al., 1975; Robinson, 1984) was used to do linear and nonlinear regression analyses.
The reason for the choice of the SPSS package was the compatibility with the computer system where the deflection basin data sets are stored.
used are briefly discussed in terms of the results.
Each of the models
If a typical set of deflection basin results are plotted on a logarithmic versus linear scale, like in Figure A.1, some guiding observations can be made as to what types of models can be used.
There is in general a tendency towards a straight line, althouih as shown, it is still slightly curved.
Based on these observations.
the following models as shown in Table A. 1, were used.
The values of the related parameters are also given as derived from the linear regression model in the SPSS package (Nie et al.,
1975) for a typical data set.
The results of these models for typical data sets are shown in
Figures A.2
and A.3.
Before even considering the statistical evaluation, it can be seen that there are some shortcominis in some of these models.
Figure A.2 illustrates that models 1 and 2 (as defined in Table
A.1) are only applicable to the area of positive curvature.
Model
2 is however able to be accurate over a wider area (10 to 300 mm).
Figure A.3 shows that if model 1 is used over a wider area than that covered by the positive curvature of the deflection basin, it can easily lead to an ill fit.
For that reason models 1 and 2
E
E z
0
~ u
10
1 lL.
W
0
16
~~
~
..
~
•••
.....
~
__ .
•• I~
x
FITTED MODEL
• MEASURED POINTS
.~
. .~.
..
,
..
..
:~~
.
FIGURE A.I
TYPICAL LOG VERSUS LINEAR PLOT OF RSD DEFLECTION BASIN MEASUREMENTS
200
HORIZONTAL DISTANCE
(mm)
FIGURE A.2
TYPICAL PLOTS OF LINEAR REGRESSION MODELS FITTED TO THE POSITIVE CURVATURE
5
0,200
....
u
W
J
tt
0,150 o
D a a
FIGURE A.3
TYPICAL PLOTS OF LINEAR REGRESSION MODELS FITTED
TO THE WHOLE DEFLECTION BASIN
l.
Y •••
0 exp
(A1 x
2)
0
10(A1x
2) or log y •••log Ao + A1x
2
Parameters for a typical data set
A ••• o
A •••
6
0,991 x 10 o
2.
3.
y •••
2
0 y •••exp (a2 x
2 ••• a1 x + a )
0 or y •••10(a2x
2
+a'1x+ao)
A •••
0,4578
0 a
•••
0,4990
0 a1
••• 0,4513 x 103 a2
••• 0,1330 x 106 a
0
••
0,4467 a1
••
0,7818 x 10 3
0,98 a2 ••• 0,2309 x 106
9 a3 •••
0,1021 x 10 were only applied to the first 200 rom.
This is covering an area wider than the normal width of positive curvature (Dehlen 1962) but it does not lead to ill fits of model 1 (see Figure A.2).
A distinctive feature of the deflection basin curves as shown in
Figure A.3, is the peakedness of the area of the area of positive curvature.
This area of positive curvature is on average less than 10 per cent of the horizontal distance of the whole deflection basin.
The Rsquare values of model 1 and 2 are an acceptable 0,99.
The goodness of fit was also calculated as follows:
T n
 E
(y  Y
)2 i=l i i n
 E (y  A)2 i=l i
*
100
% where A = Average of measured values
Y.
= Measured data values
~
Yi = Values from model fitted
The goodness
95 per cent.
of fit for a typical data set for models 1 and 2 is
Both therefore have acceptable values of
Rsquare and goodness of fit for the positive curvature region.
Models 3 and 4 are polynomial functions of the order 2 and 3.
There is no real advantage gained in accuracy when the order of the polynomial is increased above the third order.
The computation takes longer and becomes costlier too.
The goodness of fit of the second order polynomial (model 3) for a typical set of measurements is 99 per cent.
It can be seen in Table A.1
that the Rsquare values for models 3 and 4 are also an acceptably high 0,98.
This is very good, but visually it can be seen in
Figure A.3
that the deviance from the observed values in the very small area near the origin (positive curvature) does lead to some concern as to the applicability thereof for the whole deflection basin.
This tendency to give equal weight to all data points along the linear horizontal distance (x) is typical of this linear regression model used in the SPSS package.
For that reason it was decided to investigate the nonlinear regression analysis with available models that would tend to give a better description of the whole deflection basin.
Another point of interest in the vicinity of maximum deflection
(xa) is the gradient of the tangent at xa.
In Table A.2
the
gradient of the curve described by any of the 4 models is given as first order differentials.
2.
y"
A x
2 o
First order differentials
~ dx
~ dx
= A
(Exp (Alx
2
0
 2A x
0
»
2Alx
~ dx
= a . 2'2x) exp (a xl
2
+a
X o + a )

At the point of maximum deflection (xO) only models land 2 have a horizontal gradient as the first order differentials are equal to zero.
The gradient given by Models 3 and 4 are dependent on the values of the constants when xO.
This is another indication of ill fit of models 3 and 4 at the point of maximum deflection.
As indicated earlier, the nonlinear model of regression analysis used in the SPSS packaie (Robinson, 1984) tends to give equal weight to each measurement on the deflection basin.
In using this nonlinear regression analysis package the aim is then to minimize the sum of squares.
It is the sum squares of the difference between the fitted model and the observed measured points.
For this reason it is therefore important that
the unnatural "spikes should be smoothed out before curve fitting is done.
There are two options in the nonlinear regression analysis package of SPSS (Robinson, 1984) namely using the Gauss method or the Marquardt method.
The latter was selected as superior due to its shorter computing time required.
In Table A.3
the two models tested by the two options are shown with the calculated constants and sum of squares values.
Sum of squares Parameters for a typical data set
8,914 x 10
1
A ••3,321*101
A~ •• 9,991*101
3,768*103 a •• 1,066 o
3
a1 "" 1,134*10_7 a2 •• 2,796*10
As can be seen both models had been tested for curve fitting by the linear regression analysis facility of SPSS before.
Model 1 was again tested here on an area wider than the positive curvature by selecting the first 350 mm for curve fitting.
As could be expected it did lead to a poor fit as reflected in the rather high value of sum of squares.
The residuals (difference between prediction and observation) are also plotted.
Apart from giving a visual impression of the goodness of fit, it also serves as a monitor for specific patterns which indicate poor fitting models.
In Figure A.4 the residual plot of the model 1 fitting is shown.
The definite pattern confirms the ill fit.
It reemphasises the fact that model 1 can only be applied to the area of positive curvature
«
150 rom).
Model 2 (Table A.3) proved to be better suited for the fitting of the whole deflection basin and particularly the large area of
~ a:
UJ lD
~
::l
Z en
L&J en
<t u
15
5
0 10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
RESIDUALS
(X
20
16~
FIGURE" AA
RESIDUAL PLOT OF AN ILL FITTING MODEL
the reverse curvature of the deflection basin.
The good fit thereof is reflected by the low value of the sum of squares in table A.3.
The plot of residuals in Figure A.S also reflects no specific patterns indicating a good fit.
The lack in fitting the area of positive curvature in the vicinity of maximum deflection still persists as was indicated in the linear regression analysis too.
It would be possible though to use these two models of table A.3 and limit the curve fitting of the positive curvature to that by model 1 and the curve fitting of the larger reverse curvature to that of model 2 and achieve satisfactory results.
The nonlinear package of SPSS makes it possible to use relatively complex models in the regression analysis.
This gives the opportunity to look at physical models which can be adapted to the observed deflection basin.
A promising model is that of beams of unlimited length on elastic foundations with concentrated loading.
This model is described in great detail by Het~nyi (1971) and Fryba (1967).
The intention is not to give a detailed description of this theory here, but rather concentrate on the use and manipulation of the derived solutions in the curve fitting exercise.
In the analysis of bending of beams on an elastic foundation H~tenyi (1971) states that the assumption is that reaction forces of the foundation are proportional at every point to the deflection of the beam at that point based on the Winkler theory.
This theory also states that deformation exists only along the portiond±·reet.ly··under loading and was verified in experiments for a variety of soils.
Het~nyi
(1971) is quoted as follows;
II that the Winkler theory, in spite of its simplicity may often more accurately represent the actual conditions existing in soil foundations than do some of the more complicated analysis •••
11
A short description of the model is as follows; Consider an infinite beam subjected to a single concentrated force P at the a point 0, which is the origin of the axis system as shown in figure A.6.
The general solution for the deflection curve of a
(f) m
•....
.•.••.
ID
ID en o;t
~
I
0
.;r en
•
20
•
15
•
• •
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
.100
•
70
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
• •
•
•
•
•
•
•
•
•
•
•
•
•
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•
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•
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•
•
•
10 5 0
5
RESIDUALS ( x
103)
10
•
•
10
~
C
C
«
~ w
0::
::>
~ e"
IJ..
•••••

C
~
~
<: i:::
•••••
G:: l;j
~
C
~

<t)
~
§ lA,J
~
..J
Y
PA AX .
= 2 k e
(cos
AX to
S
In
A X )
DOWNWARD
DEFLECTION
BENDING
MOMENT
M=
:A eAX
(cos
AX sin
AX)
Q
=2' ecos AX
SHEARING
FORCE
FIGURE A.6
POINT LOAD ON AN INFINITE BEAM ON AN ELASnC
FOUNDATION
beam subjected to transverse loading is derived by Hetenyi
(1971) as; where y is the deflection taken as positive downwards x is the horizontal distance from the origin
C1,
CZ'
C3, C4 are constants
~ is the damping factor, and k is the modulus of the foundation expressed in kg/m
2
/m
E is the modulus of elasticity in kg/mn
I is the second moment of area of the beam
Without even going into further detail of the simplification of this model it can be seen in Figure A.6
what the similarities between the modelled deflection curve and the measured deflection basin curves are.
When the symmetry of the deflection curve and the equilibrium of the reaction forces are
Y considered this general equation reduces to;
= p
Zk e
).x
(cOSAX
+ sin~x), which gives the deflection curve for the right side (x>o) of the beam.
This correlates well with the data preparations of the deflection basin described in the preceding sections.
The form of the curve suggests that the case of no dampening can be considered for this part of the curve analyzed.
Fryba (1967) gives the solution as follows for such a situation; e
blxl
(a cosax
+ bsina Ixl)
This form is obviously similar to that derived by Hetenyi (1971.
In order to simplify the determination process of the constants in these equations, it was decided to use the following curve fitting model;
In figure A.7 a plot of a typical data set and the curve fitting is shown.
Visually it can be seen that this model succeeds in describing the observed deflection basin accurately.
The sum of squares value is low (4.15 x 103 for this typical data set) and the plot of the residuals does not indicate any ill fit.
The goodness of fit for such a typical data set is above 98 per cent.
It was found that this mode is applicable over a wide range of variances in load.
load repetitions and structural condition of pavements.
It is obvious though that although this model gives the best fit of all models tested it still tends to give an ill fit in the positive curvature area.
Although this area is very small and very peaked in relation to the rest of the deflection basin. it was decided to use the parabola of the linear models in this area of possible curvature in order to arrive at a true representation of the whole deflection basin.
z
Q
I
U w
LL
W o
E 0.2
E
Y
=
B
1 e
8
2 X
(COS
B 3
X
+ si n B
3X )
LOAD 60 kN
NO REPETITIONS x 
PREDICTED
• OBSERVED
FIGURE A.7
TYPICAL CURVE FITTING OF PHYSICAL MODEL
SUHHARY ON CONDITION SURVEYS ENHANCING
DEFLECTION BASIN ANALYSIS
A condition survey is an important input in the nondestructive testing of an analysis procedure.
In Figure B.1 it is shown how this kind of visual survey greatly enhance the understanding of the material characterization in a typical analysis procedure for overlay design.
Condition surveys are nondestuctive testing procedures enhancing the other nondestuctive testing procedures such as deflection basin analysis. In Figure 4.1 it was explained how in the South African mechanistic rehabilitation design procedure (Freeme, 1983) it is important to identify the pavement layer state.
The discussion on condition survey will therefore focus on crack and rut classification related to the deflection basin survey (see Figure B.1).
Ullidtz (1982) defines a functional and structural condition in his model on pavement rehabilitation.
He states that; "The structural condition is of no immediate interest to the road user but is is extremely important to the highway agency because the future functional condition depends on the present structural condi tion. " A visual condition survey can be seen as an aid to a proper structural evaluation.
The standard procedure for conducting a condition survey, as outlined in Draft TRH12 (NITRR.
1983), should be followed.
Normally the visual assessment precede the deflection basin survey but it is suggested that the deflection basin survey and visual assessment may be done simultaneously on smaller scale projects.
The results of both surveys should be plotted on the same scale.
By this means the obvious weak spots can be identified when other relevant information such as drainage, cut or fill transition and soil changes is taken into consideration.
Pavement Evaluation and Overlay Design Inputs raff ic
Data
Deflection
Survey
Analysis
Sections
Destr u ct iv e Testi ng
Insitu Material Sampling
1esting Lab. Testing
Pavement Class Identification
Compute Deflection Basin
Parameter Function
Compute Distress Determi nants
Fatigue Cracking
Overlay Criteria
Overlay Thickness and System Selection
FIGURE 8.1
Mechanistic overlay design flow diagram
B.3
Cracks in the existing asphalt concrete layer have a major influence on the overlay design procedure.
Normally pavements are classified as either cracked or not cracked.
However, the majority of pavements fall somewhere between these extremes.
The aim of this section is therefore to establish quantitive procedures to classify cracked pavements in order to improve the rehabilitation design procedure.
Grant and Curtayne (1982) point out that fatigue is not necessarily the cause of cracking in asphaltic concrete layers in South
Africa.
Other factors, not necessarily trafficrelated, should also be considered as being possible causes of premature cracking
(Grant, et al (1979).
Pronk and Buiter (1982) indicate that with full depth asphalt pavements, even in the Netherlands, cracking does not necessarily begin at the bottom of the asphalt layer.
Grant and Curtayne (1982) therefore stress that a study of the past behaviour of the pavements can provide good clues in this respect.
The preceding statements are to indicate the complexity of crack mechanisms of asphalt concrete layers.
Different reasons for cracking are therefore discussed in order to arrive at a classification for cracked pavements.
The aim of this is purely to simplify the analysis of such a pavement by using the deflection basin parameters in the mechanistic approach.
First it is suggested that the difference in basic crack mechanism, due to the difference in pavement structure be considered.
For the South African condition it is suggested that on the grounds of asbuilt plans or matericiTsamptingprocedure (Figure
B.1), a flexible pavement under survey be classified according to the basic TRH4 (NITRR, 1985a) catalogue, i.e.
(a) granular base pavements
(b) bitumen base pavements (tar as an alternative)
(c) cemented base pavements.
This basic classification is taken a step further by Freeme (1983) by relating the timedependent behaviour of different pavement types to the concept of equivalent material state illustrated in
Figure B.2.
It is explained in Chapter 3 how the measured deflection basin parameters can be used to accurately identify any such pavement behaviour state.
Next, the degree of cracking should be defined.
In the light of work done by Kilareski et al. (1982) and Treybig et al. (1978), it is suggested that the AASHO definition of cracking could be applied.
Jordaan and Servas (1983) give a very clear description of three types of cracking and how it should be calculated.
These types are crocodile or map or block cracking, longitudinal cracking and other crack patterns or combinations of the preceding types.
For these types each 100 m of road length is classified as being in a sound, warning or severe condition.
This depends on the percentage of 100 m being cracked and the road category.
Crack conditions can be improved by crack filling and repair of the low percentage of severe cracking of the defined categories or crack types.
The decision to repair cracks should be based on economic comparisons, but it is obvious that crack repair will improve possible crack attenuation behaviour in general.
Koole
(1979) suggests though that an overlay design based on the severe condition of cracking might in some cases be the most economical in the final analysis owing to the expensive nature of procedures to upgrade the pavement in regard to the crack condition outlined above.
In the final level of crack classification more sophisticated methods should be considered.
This normally consists of analysis procedures associated with the overlay design analyses.
Various researchers, such as Molenaar (1983) and Coetzee and Monismith
(1979) suggest the use of fracture mechanics principles and finite element computer programs in the analysis stage.
In order to use these procedures though, the previous crack classification would have to be elaborated in order to establish average values of crack width too.
Molenaar (1983) states the following:
I
19404 4760/9
B.D.
STATE ...
APPROXIMATE DEFLECTION
LEVEL (mm)
EXAMPLES OF CHANGE
OF STATE OF DIFFERENT
PAVEMENT TYPES
TYPICAL EXAMPLES
IN PRACTICE
VERY STIFF
0,2
I
STIFF
0,4
I
. FLEXIBLE
0,6
I
VERY FLEXIBLE
CONCRETE ~
CEMENT TREATED BASE PAVEMENT
•
CRUSHEDSTONE OR BITUMEN TREATED
BASE OVER
CEMENT TREATED SUBBASE
BITUMEN TREATED BASE OVER
GRANULAR SUBBASE
GRANULAR BASE IGRANULAR
SUBBASE.
LOW SUBGRADE
CBR VALUE
CONCRETE ROAD N2
HOORNSNEK (TVU ; BRONKHORSTSPRUIT P67/1 (TVU; N3 SWINBURNE (OFS)
P157/1 a PI57/2 JAN SMUTS AIRPORT nVU;PARADISE
N3 MARIANNHILL (NTU
P205/2 GI LLOOL Y (TVU
VALLEY (NTU
KOEBERG (CAPE)
PI23 MAGALIESBURG nvu
P6/1 BABSFONTEIN (TV L)
FIGURE B.2
DIAGRAMMATIC REPRESENTATION OF THE TIME DEPENDENT BEHAVIOUR
OF DIFFERENT PAVEMENT TYPES
(Freeme,
/983)
"Although the fracture mechanic's approach has the potential to be an excellent tool in solving the reflection crack problem, it has not gained very much popularity.
In fact it can be stated that it is still a research tool and that its practical application is limited to only a few cases."
Recently the monitoring of crack movements, as described by Rust
(1984), has become another viable method that may be associated with the classifications outlined above.
The Crack Activity Meter
(CAM) that was developed can measure amongst others the defined total crack movement.
Crack activity or total crack movement normally has the typical peaking behaviour with axle repetitions as shown in Figure B. 3.
Rust (1985) was able to determine that for a flexible pavement with a cemented base and under specific conditions, there is a good correlation between block size and crack movement.
The data indicated that there is a critical block size below which the crack movement increases markedly with further decrease in block size.
Typical results are shown in
Figure B.4.
These concepts can be used effectively to enhance the crack classification as given above.
In Appendix E the good correlation between the measured crackactivity and measured deflection basin parameters is illustrated by means of an example. As will be shown there this greatly enhances the rehabilitation analysis procedure.
One of the major aims of a rut survey is to determine the amount of material needed for the levelling of the existing rut before an overlay is applied.
This is all related to ride comfort (PSI values) and, in wet conditions in particular, to rider safety.
The extent of rutting is generally used in overlay design as a major criterion of permanent deformation and the structural state of the pavement.
The general procedure is to limit rutting in overlay designs by limiting the vertical subgrade strain (e: ).
vs
This approach was originally developed by Dorman and Metcalf
o lD
~
I
V
·v
I o
If) ....
If)
If)
•
x
JOINT 132
JOINT 131
WHEEL LOAD: 40 kN
E
=
I
Z llJ
::E llJ
>
0
::E
:l<::
U
<t a: u
...J
<t
I
0
I
400
200
...•.
••.•x
.......
..•..
..•..
....•.
..•..
•....
....•.
,
•....
"X o o
200
REPETITIONS
(x
400
10
3)
FIGURE B.3
CHANGE IN TOTAL CRACK MOVEMENT DURING HVS
TESTING ON THE N2 CONCRETE ROADSECTION 258A2
(Rust
I
1984)
14045097/2
BS
400
300
~
0
«
0::
0
.•..•
E
~
Jz w
:IE w
>
0
:IE
200
100
.\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
.,
,
,
•
•
•
.',
"
•
"'
,
......... ........
,
,
"........
• •
.
•

.....•..
...
.


•
•


•

•
.

.
•
•
•
•
~

o o
4
BLOCK SIZE
(m)
FIGURE 8.4
CORRELATION BETWEEN CRACK MOVEMENT AND BLOCK SIZE ON THE
MR 27 (Rusf,1985J
.
tJ:l
00
(1963) in their analysis of the behaviour of the test sections of the AASHO road test.
It is should be noted that rutting is not only related to the subgrade but that contributions also come from the various layers in the pavement.
For this reason Koole (1979) mentions that the rut in the asphalt concrete layer should be treated separately.
The South African experience also indicates that such a direction should be followed.
Freeme et ale (1982a) indicate that better characterization of the bitumen layer in terms of volumetric and shear properties is necessary to accommodate this deformation phenomenon in the bitumen layer.
Maree et ale (1982) show that for granular base pavements tested with the Heavy Vehicle Simulator (HVS). most of the permanent deformation took place within the granular base and subbase.
The subgrades never meaningfully contributed towards the total deformation and were always well protected.
In the same report Maree et ale (1982) illustrate the strong correlation between cracking, excessive rain, moisture intrusion and deformation for typical granular base pavements; this is shown Figure B.S.
The preceding statements make it obvious that a more qualitative classification of rutting is needed than just a report of the average rut.
In line with the classification outlined in the previous section on cracking, it is suggested that the pavement structure classification as defined be used also.
In fact it is reemphasized that no indicator like rutting or deflection should be used in isolation.
The concept is clearly illustrated by
Freeme (1983) in Figure B.6
where various indicators of the behaviour of typical granular layers are shown.
A further practical classification is needed to discriminate between various mechanisms of permanent deformation.
Molenaar
(1983) classifies two types of rutting (see Figure B.7).
The first type is that without lateral displacement due to densification.
The second type is that with lateral displacement due to
Prandtl type of shear deformation.
This ties in with the previous discussion on the South African experience.
Grant and
z
Q ti
~ 10
Q:
~
W o
INGRESS OF WATER
\ \
\
HIGH QUALITY
GI STANDARD
FIGURE 8.5
SCHEMATIC DIAGRAM OF THE RELATIVE BEHAVIOUR OF
GRANULAR MATERIAL OF DIFFERENT QUALITIES
(Moree, of 01., 1982)
.......
o w r
~
I
~
I o
~ lI'L _
E
E
15
Z o
~ 10
~
0::
~ 5
1LI o
DENSIFICATION
I
I
I
I
I
I
I
PHASE 2
STABLE STATE
WATER AND WATERI
SUSCEPTIBLE
MATERIAL
I
I
PHASE 3
I
I
EFFECT OF INGRESS OF WATER
~ tv<1:
~'i"
RATE OF INCREASE OF
<lot/;
e,
0'< DEFORMATION CAN REDUCE
AGAIN IF WATER IS REMOVED
"
~(j
RATE OF INCREASE DEPENDENT ON
QUALITY OF MATERIAL
MOISTURE· CONDITIONS
AND STA BLE
•• ESOs OR TRAFFIC
(a) PERMANENT DEFORMATION
~
I
Ua: lLIlL1
I)
L&.<t
1LI1 o
INGRESS
WATER zJ:
1LI!::
::::;~
(f) lLI
0::
ESOs OR TRAFFIC
(b) RESILIENT BEHAVIOU R
IF WATER IS REMOVED
DEFLECTIONS CAN
~REDUCE BECAUSE OF

INCREASE IN RESILIENT
MODULUS OF LAYER
....•.


DEFLECTION REMAINS LOW
IF LAY ER NOT SUSCEPTIBLE TO WATER e.g.
CRUSHEDSTONE BASE OR WATER
BOUND MACADAM
••
~
(f)
:3
:> o
~ 250
0..
z
2 u~
00::
IlLI
Z lLI
0..
~
g
m
........
I
Z lLI
I
(f) lLI
0:: 0
ESOs
(c) CHANGE IN MODULUS OF
AND WATERSUSCEPTIBLE
MATERIAL
/MATERIAL NOT SIGNIFICANTLY
I
I
I
I
I NGRESS OF WATER
~WATER
,..,.
TO THE INGRESS SUSCEPTIBLE
OF WATER





REMOVED
OR TRAFFIC
CEMENTED LAYER
I
INGRESS OF WATER
I
AND WATER
SUSCEPTIBLE
I
MATERIAL
I
I
I
.,.,.......
WATER~"""
REMOVED
_
MATERIAL NOT SIGNIFICANTLY
SUSCEPTIBLE TO THE INGRESS
ESOs OR TRAFFIC
(d) STRENGTtl BEHAVIOUR
FIGURE 8.6
••
INDICATORS OF THE BEHAVIOUR OF GRANULAR LAYERS
..
IE r eeme. / !lE31
~
~~
LORIGINAL
· r
· r
I
......•.....•.•
~
Type
A
~
SURFAr PROFILE
I
·
1
·
Rutting without lateral displacement of the material. This type of rutting is due to densification of the material .
I
·
· r
t~~
Type 8
_I
.
I
·
~.;I
Rutting with lateral displacement of the material.
Rutting can be judged to be a Prandtl type of shear deformation.
FIGURE 8.7
TYPES OF RUTTI NG WHICH CAN 8E DISCERNED
( Molenaar, 1983)
Curtayne (1982) note that shear in the subgrade is characterized by wide rutting.
Shear in the base layer is characterized by narrow ruts with displaced material appearing like a mound adjacent to the rut.
From the visual survey therefore a classification of the type of rutting that exists may be made. which will strongly influence the overlay design analysis. The Draft TRH12 (NITRR. 1983) give clear indications for rut criteria related to pavement class and pavement type. It is suggested that those criteria and those suggested by Jordaan and Servas(1983) be followed.
At any specific moment, an existing pavement has a certain amount of accumulated damage done to it by repeated traffic loading.
There is normally also a certain amount of remaining damage which the existing pavement can undergo before failure.
The severity of the damage caused by each repeated traffic loading depends on the structural strength of the existing pavement.
This is usually expressed in terms of the equivalent number of standard axles
(E80s).
If the magnitude of the critical strains is reduced, then the existing pavement can carry a larger number of standard axle loads (E80s).
The function of an overlay is therefore to reduce the magnitude of these critical loadinduced strains or stresses, depending on the distress determinants being used.
Remaining life has two meanings.
Without an overlay a pavement normally has remaining life and with an overlay a pavement has a remaining life, that is usually lengthened or prolonged.
For this reason "remaining life" will refer to the remaining life of a pavement without an overlay.
In the literature remaining life is usually analysed on the basis of the phenomenological theory of cumulative damage.
Attempts to relate the structural condition, based on deflection basin measurements, in a different way to the life of the pavement, will also be discussed.
The phenomenological theory of cumulative damage is also referred to as the linear summation of cycle ratios.
This was advanced by
Miner (1945) to predict the fatigue life of metals subjected to fluctuating stress amplitudes.
Monismith et ale (1966, 1969) used it to estimate fatigue life of bituminous layers in pavement structures and established it as an acceptable and useful relationship.
Let n. ••number of applications at stress or strain level
1
N. ••number of applications to failure at stress or strain
1 level
D.
•• damage due to N. number of applications at stress
1
1 or strain level
Then the damage, Di, is defined as the stress or strain cycle ratio, i.e.
D
1
.
= n
1·
N.
1
Failure will occur when D. = 1.
1
Let r = number of different stress or strain levels involved
D = cumulative damage due to number of applications at different stress or strain levels
Then the cumulative damage, D, is stated as the linear summation of cycle ratios, i.e.
r
E D i=l i r
=
E n i i=l N.
1 or r
E i=l n.
2=
N.
1
1
Snaith et al. (1980) use the distress determinants vertical sub grade strain (€vs)' and maximum horizontal aspahlt strain (ERA)' as discussed in chapter 4 and 6 , to determine damage due to rutting deformation and fatigue cracking respectively.
For both forms of damage the strainlife relationship is given by the general equation:
It is therefore possible to apply the cumulative damage theory to both forms of damage.
The accumulation of damage from repeated applications at various strain levels is illustrated diagrammatically in Figure C.1.
In Figure C.1(a) the strainlife diagram is shown with a typical strainlife curve, lk.
On this curve a strain level
E
1, for example, corresponds to a life N1.
Lines ab, cd, etc., represent n1 applications at strain level
E l, and nZ applications at strain level
E
Z'
etc.
These lines, represented by arrows, are called damage paths.
The dashed lines, bc, de etc. are called isodamage lines.
If the amounts of damage at band c are the same, then
This is represented more simply in a damagelife diagram (see
Figure C.1(b».
The damage scale ranges from 0 to 1.
The damage paths can be plotted continuously as shown in Figure
C.1(c).
In this way, the cumulative damage arising from repeated applications is determined in diagrammatic form.
In practice the number of repeated applications (n.) is expressed
1 in terms of the equivalent number of standard axles (E80s).
This reduces the analysis to only one strain level to determine remaining life.
In Figure C.1(a), therefore, at strain level
E
1 the damaged or consumed life is nl and total life is N1.
Remaining life at this strain level is equal to:
Alternatively, damage (D1) is often expressed as previously defined and remaining life (R1) is then:
E', a b d
.,
'"
"' ••..
_
..

DAMAGE PATH
ISODAMAGE LINE
I n lll n4
N
4
N"
N4 h
N....

~ DAMAGE PATH
ISOSTRAIN LINE
(c)
DAMAGEPATH
DIAGRAM
FIGURE C.I
GRAPHICAL PRESENTATION OF CUMULATIVE
DAMAGE THEORY (Snaith , et a I., 1980 )
R
1
=
1D
1
=
1
n 1
N1
Using the same distress criteria, vertical subgrade strain (e vs
) an d maximum horizontal asphalt strain and (eRA)' Anderson (1977) also used this theory to determine remaining life.
It is pointed out, though, that future environmental or traffic changes cannot usually be foreseen and therefore such a procedure should be seen as a guide only.
In considering the remaining life of a pavement with rutting due to permanent deformation, Anderson (1977) reasons that the damaged life or consumed life will be nullified when the surface deformation is removed by an overlay.
Koole (1979) supports this view by Anderson (1977) in his description of the Shell overlay design method.
The remaining life of a pavement with fatigue cracking is determined in accordance with the description by Snaith et ale (1980).
Treybig et ale (1978) also use the theory of cumulative damage in order to determine remaining life for a pavement with fatigue cracking and rutting due to permanent deformation.
As mentioned in
Appendix B, however, the cracked state of the existing pavement is taken into consideration in determining the material parameters
(E asphalt).
Chapter 4 described how these material parameters are used to determine the distress determinants.
In a pavement with fatigue cracking the maximum horizontal asphalt strain (ERA) is calculated and used to determine the remaining life in terms of standard axle (E80) repetitions, as described by Snaith et ale
(1980).
It was shown in Chapter 6, Treybig et ale (1978) consider the contribution of all the structural layers to rutting due to permanent deformation by determining the various stresses and strains of each layer.
It is obvious that Kilareski et ale (1982) only considered fatigue cracking when determining remaining life.
The strain (eRA) need not necessarily be determined, but as shown in Figure C.2 the
deflection basin parameter.
surface curvature index (SCI). is related to the number of equivalent singleaxle loads (EAL).
In this case the structural number has also been determined.
based on the AASHO Design Procedure (for the various test sections).
The 10 per cent fatigue cracking line is the same form as described above for the general relationship.
N
=
A(l)b.
e:
The equation for remaining life is as described above. namely (N1  n1).
Kilareski et al. (1982) advance this one step further by relating remaining life (in terms of equivalent axle loads) to the SCI for various structural numbers (pavement strengths).
as shown in Figure C.3.
Residual life determined from deflection measurements alone does not lead to satisfactory results.
Koole (1979) states: "It is not possible to determine the residual life of a pavement solely from deflection measurements".
The reasoq lies in the fact that the change in a structural parameter.
for example elastic modulus (E).
with an increase in load repetitions shows a sharp decrease in value initially but thereafter there is a long period during which virtually no change occurs and only at the end of the structural life is there a definite sharp decrease to distress.
measurements also reflect this typical behaviour.
Deflection
However.
it is possible to relate early life deflections empirically to the critical life of particular types of pavement structures.
as shown in Figure C.4 using work done by Lister and Kennedy (1977).
Koole
(1979) also mentions that original design life can be determined from FWD deflections.
A "crude" test on consumed life is to take
FWD deflections between the wheel tracks.
If the deflections measured in the wheel tracks.
are significantly greater than those measured between the wheel tracks the pavement is approaching the end of its service life.
Pronk and Buiter (1982) mention the procedure in which the decline in effective layer thickness is related to the structural strength.
This forms the basis of the structural performance model developed by Molenaar (1983).
This principle is shown schematically in
Figure C.5 where equivalent layer thickness (H ) decreases in e

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1000
700
500
400
300
200
100
80
60
Section No.
• •
Structural No.
H (2.70)
10% Fatigue Crocking Line
8 (:3.14) 9(3.58
)
~
14 (3.65)
1d (3.72 )
___
~,..,...
Ic (3.94) __ .•, "
2 (4.38) "
7 (4.74)••.•
I x 10s 2 3 4 6 8 Ix 10
6
2
18kip (80kN) Equivalent SingleAxle Loads
3 4 6
FIGURE
C.2
VARIATION OF SURFACE CURVATURE lNOEXWITH
EAL.
(Kiloreski, et
01.,1982)
l
~ 3.0
~ 2.0
W lL.
l
1.0
~
z
0.7
w
~ w
~
(,!) z
z
0.2
<t
~ w a::
O. I
0.07
0.05
STRUCTURAL NUMBER, SN
5.0' 4.5
4.0
3.5
3.0
50 100 150 200 250
SURFACE CURVATURE INDEX, SCI<l6
6
IN.)
300
FIGURE C.3
REMAINING PAVEMENT LIFE BASED ON
FATIGUE CRACKING FOR BITUMINOUS
CONCRETE PAVEMENTS WITH SUBBASE.
(Kilareski, et aI., 1982)
14044760/38
200
150
N
I
0
)(
E
E
.
Z
u w
I
LL
W
0
100
80
60
50
40
30
0
•
•
0
ROAD BASE
&
Hot rolled asphalt x
"
•
Dense bitumen macadam
•
Dense tarmacadam
Medium textured tarmacadam
Open textured tarmacadam
Readings still sound
AO
~
.yAy
• A
• A y
A
0,2 0,3 0,4 0,6 0,8 1,0 1,5 2 3 4 5 6 8 10
CUMULATIVE STANDARD AXLES (x 10
6)
FIGURE C.4
RELATION BETWEEN DEFLECTION AND CRITICAL LIFE OF
PAVEMENTS WITH BITUMINOUS AND TAR BOUND BASES
(Lister and Kennedy, 1978 )
15 20
.
n
0
I
Z
W
J
<X:
>
~ o
W
(f)
(f) w z
:::c: u
:c
I~
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LOAD REPETITIONS n
FIGURE C.5
HYPOTHESIZED DECREASE OF THE EQUIVALENT
LAYER THICKNESS (He) WITH RESPECT TO THE
NUMBER OF LOAD APPLICATIONS (n).
relation to the number of load applications(n).
The structural condition of the pavement can be characterized by means of the structural condition index p. which is defined as:
P = H /H ecn eco where H ecn
= equivalent layer thickness after n load applications corrected for temperature and environmental fluctuations
H eco
= equivalent layer thickness just after construction corrected for temperature and environmental fluctuations
In order to determine H • deflection values between the wheel eco paths are measured as described above.
Molenaar (1983) defines Heco values determined in this way as "candidate" H eco values since they would have been subjected to some loading between the wheel paths.
The amount of future deterioration depends on the expected number of load applications.
the structural condition index P and the shape of the deterioration function characterized by Sl N.
og
Values for Sl N should also be determined by means of deflection og measurements.
Sl og
N can be calculated as follows: where
2 2 2 S2
= a1 b1 S log He
+ l.o.f(l N 1 ) og  oge: a1 = slope of fatigue relation b1 = slope of H versus log e:relation (=2) e
S2
1.o. f.
= lack of fit of the equation used to describe the fatigue relation
(=0,16)
In Figure 4.10 the typical relationship between H and surface e curvature index (SeI) is shown from results of deflection basin
z
0
I
...J
<r
0::
:::>
Iu
:::>
0::
I
en
0 z
0
U w
0 z
x a..

1,0
0,8
0,6

f3
S\OgN
0,2
REPETITION RAT\
0,4
° n / N
FIGURE C.6
COMPARISON OF THE THEORETICALLY
DERIVED STRUCTURAL PERFORMANCE
MODEL AND THE EQUIVALENT LAYER
THICKNESS DETERIORATION MODEL
(Molenaar, 1983)
plotted in relation to deterioration (n/N) and the influence of
Sl N can also be seen.
og
Molenaar (1983) takes this even further by calculating P and SlogN directly from deflection basin parameter values such as surface curvature index (SCI) as follows:
P
=
(SCI /SCI )d o n
S2 log
N
= d2 2 2 2
1 c1 S 10gSCI+ Sl.o.f
(log Nlog
€) where SCI o
=
SCI at time of construction
SCI n
=
SCI after n load applications d1
= absolute value of the slope of the SCI versus He relation (a reasonable value is
0,53) c1 = slope of the 10g(SCI)in relation to log N (=0,943)
All other variables have been defined before.
However.
Molenaar
(1983) warns as follows:
"Although the procedure to calculate P seems very simple, one should be aware of the fact that in a number of cases the ratios H /H ecn eco and SCI /SCI might be larger than one.
o n
Remaining life is determined by this procedure as illustrated in
Figure C.7.
Molenaar (1983) modified the work done by the Belgian Road Research
Centre.
He uses the following equation for permanent deformation model: where u· permanent deformation (m) p

¢
......
o
CD
~
¢
~
I
I o
~
...
Z o
Io
Zo~
~ [j
0.9
<:to a:
Z
::>
I
U
::> a:
I
0.8
en
0.75
0.5
REPETITION RATIO n/N
FIGURE C.7
PROCEDURE TO ASSESS THE REMAINING
LIFE (Molenaar,1983)
u = elastic deformation (m) e
By means of regression analyses of a typical threelayered pavement system Molenaar (1983) used the BISAR computer program to arrive at values of bo' b1 and n for the various interfaces between the layers.
The elastic deformation at the pavement surface must be known in order to be able to determine the elastic deformation of the top layer.
This deformation due to dual wheel loading can be estimated from the maximum deflection (6 ) value of the falling o weight deflectometer (FWD) by using the following equation: log Ue surface = 0,09+0,948 log 6
0FWD
The elastic deformation of each layer can be calculated by subtracting the deformation at the lower interface from the deformation at the upper interface.
The permanent deformation can then be calculated by means of the permanent deformation model with constants shown in Table C.1.
A correction factor is applied to relate observed rut depth to these calculated values.
By these means rut depth can be related to load applications (n), and consumed rut life can be determined by defining a terminal rut depth of for example 20 mm.
In chapter 4 and 6 it was concluded that the current mechanistic design procedure in South Africa using distress determinants vertical subgrade strain (€ ) and horizontal asphalt strain (€h ) vs a is a sound one.
Proper fatigue relationships have been established for these parameters.
This makes the use of the linear summation of cycle ratios applicable to both distress criteria: fatigue cracking
=
(l)b),
€ and deformation rutting.
The generalized relationship, (N described by Snaith et al.
(1980) can thus be used to
TABLE C.1.
Values forob and1b to be used in the calculation of the permanent deformation (Molenaar.
1983)
=
U *b n b
1 e
0
Bituminous layers
5 000 (summer)
Stone base
U *4.49nO.25
e
U *2nO.3
if n<0.12 m e
U *2nO.2
if n<0.12 m e
500
Lean concrete base
1 500
Granular subbase
Subgrade
U *2nO.3
e
U *(1+0.7
logn) e
200
5. 1O. 20. 40 determine remaining life for both distress criteria.
The more critical value can then be used in the selection of an overlay, as described in Appendix D.
Although Freeme et al. (1982a) give a fundamental basis to rehabilitation design in their description of the mechanistic design procedure.
it is felt that. particularly in the case of establishing criteria to determine consumed life due to rutting, some advances can be made. This would again be possible with the information available from HVS tests and observed field data.
In this regard the approach by Treybig et al. (1978), where the deformation contributions of each layer is better rep~e$ented by~_ the computed stresses and strains of each layer, should be pursued with the available data.
It is clear too that the approach to relate the remaining life of the pavement to other structural indicators such as the equivalent layer approach shows much promise.
The structural performance model suggested by Molenaar (1983) was developed specifically for a threelayered pavement structure and therefore it is obvious that it would not be possible to use this approach in all cases.
Instead it is suggested that, with the previously mentioned information available on pavement performance in South Africa, the performance model be established with values determined from regression analyses.
This approach would then take into consideration factors
such as the deflection basin measuring device, deflection basin parameter selected and pavement structure classification described previously.
The model relating permanent deformation and elastic deformation to the number of load applications seems a sound approach.
It would also be possible to establish these relationships with the regression analysis of the information available for the South
African condition.
This section is a logical continuation of the discussion in Appendix
C.
In general, the decision to overlay a pavement under analysis will be based on criteria related to the remaining life or consumed life.
The distress criteria, fatigue cracking and permanent deformation rutting, are considered separately to determine the remaining life of the pavement.
The decision to overlay the pavement is based on the more conservative of the two criteria, but both criteria are checked again to ensure that the prolonged life
(remaining life after the overlay) would indeed be achieved.
As in any situation where various possible alternatives are generated, sound engineering judgement is influenced by economic considerations.
The latter type of decision strongly indicates the typical considerations of a maintenance or pavement management programme and should be viewed against that broader background although the focus here is on a project level based on deflection basin related criteria.
Snaith et al. (1980) describe how on the basis of the theory of cumulative damage, the remaining life can be determined.
In general this remaining life, as described in Appendix C, would be expressed as: R1
=
N1n1 or R1
=
1n1/N1.
Snaith et al. (1980) do not mention any specific criteria related to this remaining life for decisions to overlay or not.
Anderson (1977) bases the decision to overlay or not on the length of the remaining life.
If the anticipated or estimated future traffic is more than the remaining life, an overlay is needed.
If the remaining life is more than the anticipated traffic over the functional life of the pavement, no overlay is needed.
An overlay may be required for other functional reasons such as improving the skid resistance of the riding surface.
It is in this regard that Anderson (1977) states that even a nominal thickness of asphalt concrete placed on an existing pavement gives the pavement a new "life" by removing the surface deformation.
"There is no theoretical or practical
evidence which suggests that the permanent deformation which existed before rehabilitation will affect the future performance of the pavement."
In general Anderson (1977) does support the analysis procedure described by Snaith et al. (1980).
For the generalized fatigue relationship (N_(l)b) the aim of an overlay would be to reduce the e: strain level
(e: ) to the level where the anticipated traffic would vs meet the prolonged life or remaining life after overlay.
This process is shown in Figure 0.1
and in a more general form in Figure
0.2.
The formulation of the fatigue relationship considered by
Treybig et al. (1978) (as discussed in chapter 6 and Appendix C) is obViously more complicated.
Although no specific mention is made of any criteria for overlays related to remaining life the reasoning above was evidently followed.
Molenaar (1983) does not use his permanent deformation model (see
Appendix C) in his proposed overlay design.
It is obvious though that this model, if properly calibrated to field performances, would also be able to provide the same criteria based on remaining life as described in Appendix C.
If an overlay is needed, the aim would be to reduce the elastic deformation (U ) and resulting permanent deformation (U ) of each layer in order to meet the required prolonged life.
Remaining life (N 1 n 1) compared with the anticipated or future traffic is the general criterion for overlays, based on analysis using the cumulative damage (linear summation ratio) theory.
This has already been briefly described on the basis of the discussion by
Snaith et al. (1980) (see Appendix C and sections 2).
In considering the previously defined rema1n1ng life, Anderson
(1977) also considers the cracked state of the existing asphalt concrete layer and whether the pavement has an asphalt concrete layer when establishing criteria for considering an overlay.
remaining life is automatically zero if the pavement is cracked
The
~
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I o
~
N
.••..
o
U)
•.....
~.
_0_
:tI~
:'4.
0
 
0_ t
DOl
I
I.
FIGURE 0.1
CHANGES IN STRAIN LEVELS DUE TO OVERLAY.
2 "
,
"
"""
,
"
'
.••..
,
r>
4
O·
ISOSTRAIN LINE €2
(b) Damage Life Diagram
(c) Domage  Path Diagram
NOTE: B.O.  BEFORE OVERLAY A.O.  AFTER OVERLAY
FIGURE 0.2
DAMAGE PROCESS IN A PAVEMENT
STRUCTURE WITH A SINGLE OVERLAY.
( Snaith, et 01., 1980)
and warrants consideration for an overlay, or if there is no asphalt concrete layer yet.
If the remaining life is less than the anticipated traffic an overlay may be considered.
If the remaining life is more than the anticipated traffic no overlay is needed.
When an overlay is considered as was discussed in section 2 (referring to Figures D.1 and D.2), the aim would again be to reduce the strain level
(ERA) to accommodate a prolonged life or remaining life after the overlay, which would meet the required anticipated traffic life.
Analysing various pavements in this way, Anderson
(1977) arrived at characteristic curves as shown in Figure D.3.
In this figure remaining life is expressed as a percentage of the overlay thickness.
The latter value of overlay thickness corresponds to the reduction in strain level
(ERA)'
Comparing these results with those of a fully cracked asphalt concrete layer with no remaining life, Anderson
(1977) concludes that it will always be more economical to neglect any existing asphalt when the remaining life is below 75 per cent.
In this overlay design procedure, a "critical" remaining life of 50 per cent was adopted, this being the point at which the existing life is disregarded in designing an overlay.
This approach, based on the fatigue relationships described in chapter 6, was also followed by
Monismith and Markevich
(1983).
The approach by Molenaar
(1983), using the structural performance model, obviously differs from the one described above.
Molenaar
(1983) is quoted as follows:
"Although Miner's law is applicable to the development of one crack, further extension of cracks is dependent on the redistribution of the stresses, and in this case Miner's law may not be fully applicable.
Furthermore Miner's law defines a clear failure condition which occurs at e.g. the fracture of a test specimen.
Such a failure point does not exist in the case of pavements.
A
100 per cent cracked pavement surface can still be used as a reasonable driving surface unless large deformations and/or potholes occur.
Therefore a straightforward use of Miner's law in the estimation of overlay thicknesses is not considered to be a proper approach, since this will result in an unrealistic overlay design especially in those cases where Miner's ratio comes close to

C f/) f/)
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.J::
(,)
f/)
Q)
9
8
7
(,)
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~
0
~
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>
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6
5
4
3
10
2
12
II
t*
t Case 3
~
*
Case 2 t t~t Case 1
,t
Case 5
1000/0 t
t*
Case 4
25% 500/0
Remaining Life
750/0
FIGURE 0.3
EFFECT OF REMAINING LIFE ON OVERLAY
THICKNESS(Anderson, 1977)
This supports the reasoning of Anderson (1977), but also points to the possibility of the structural performance model being used to give a more realistic estimate of the structural life of a bitumen pavement.
Molenaar (1983) does not give any specific indication of criteria for decisions on overlays.
It is evident from the reasoning, however, that the remaining life determined in this way, would also be used, but with different preconditions.
The two distress criteria, fatigue cracking and permanent deformation rutting have deliberately been considered separately.
The reasoning behind this is explained by Koole (1979):
"In determining the thickness required for an overlay, the subgradestrain and asphaltstrain criteria should be considered.
separately; it is quite possible that the design criterion that did not govern the original pavement design will become limiting for the overlay thickness."
In this section an overlay thickness is thus decided upon by means of the limiting life of the two defined criteria described in section 2 and 3.
The resulting lower distress criteria parameters
(ERA and E ) are usually calculated for the possible thicknesses vs considered.
Anderson (1977) calculates these relationships for the various thicknesses of overlays by means of the techniques described in chapter 4.
This is shown in Figures D.4 and D.5 for reduction in subgrade strain (E ) and asphalt tensile strain (ERA)' In vs
Figure D.3 only pavements with more than 50 mm of asphalt concrete prior to overlaying are considered.
The reason was discussed in chapter 6 and in Figure 6.2 what the effect of relatively thin asphalt concrete layers (50 to 75 mm) on tensile strain in asphalt concrete was shown.
From the quotation by Koole (1979) above it is obvious that an overlay of for example 25 mm on the existing 25 to
40 mm of asphalt for rut requirements, could in fact shorten the remaining life of the fatigue cracking requirements.
The desired
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""V',
'"T "" v

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I
0
6
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..•..•...
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en
0
~ c c

5
4
:J

0
"0 c
0
Q)
0:: en
.0
:J
en
c
3
2
8
Thickness of OVerIOYf..
5
2 4 6
Subgrade Strain Prior to Overlay (in
8
lin
x 10
4 )
10
FIGURE 0.4
REDUCTION IN SUBGRADE STRAIN DUE TO OVERLAY (Anderson, 1977)
.
t:l
'I
i fO 44 7 60/45
V
I o
2.5
)(
C
"'

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en c:
0
•..
0
.s:::.
Q.
en
0
1.5
1.0
::J
'0
4)
o
0::
0.5
Thickness of Overlay (inches)
234
Asphalt strain prior to overlay (in/in x 10
4)
FIGURE 0.5
REDUCTION IN ASPHALT TENSILE STRAIN DUE TO OVERLAY
( Pavements with more than 2" of asphalt concre~e prior to overlaying)
( Anderson
1
1977 )
.
t:'
00
reduction in strain level can also be expressed in terms of the selected deflection basin parameters, as shown in Figure D.6, according to Anderson (1977).
Similarly the desired lower deflection basin parameter such as surface curvature index (SCl) can be related to a higher equivalent layer thickness (H ) (see e
Figure 4.10) according to the analyses of Molenaar (1983).
Treybig et al. (1978) established the most comprehensive procedure for considering the effect of fatigue cracking and rutting simultaneously.
This is shown in Figure D.7 where the existing asphalt concrete layer is regarded as uncracked.
The overlay thickness required, is determined by selecting the thicker of the two thicknesses related to the various criteria for the desired load repetitions.
Koole (1979) also describes how three separate overlay thicknesses are determined.
This includes the previously discussed criteria for fatigue cracking and rutting, and also a method of determining thickness based on the assumption that the existing pavement has deteriorated to such an extent that the asphalt concrete layer is treated as a granular layer and the overlay as a "new" asphalt concrete layer.
The latter approach is also suggested by Thompson and Hoffman (1983) when the asphalt concrete layer displays interconnected Class 2 cracking.
Remaining life in relation to the distress criteria, rutting and fatigue cracking, is the main criterion in the consideration of overlays.
The remaining life determined by methods described in chapter 6 was determined for each of the distress criteria separately.
For the rutting criterion the views on remaining life vary considerably.
The view that remaining life is completely restored by an overlay removing the deformations is Widely accepted in overlay design.
Using the various models discussed in Appendix C it is possible to determine the prolonged life by lowering the
:c u z

120

110
>
<!
....J
0:::
W
100
>
90
0
0
Iw
::>
0
80
70
N
0
60
I
0
0
50
z
40

Iu
30
::>
0 w
0:::
20
OVERLAY
THICKNESS o
10 20 30 40·50 60 70 80 90 100 110 120 130 140 150
DO 
0
12
PRIOR TO OVERLAY (INCH)
FIGURE 0.6
REDUCTION IN 0
0
0
12
DUE TO OVERLAY
(Anderson, 1977)
.
t1
0

;;;8
Cl) c
~ o
.J::.
I
:>; o
~
Cl)
Cl)
.J::.
o c:
•.....•• en6
(J)
4
2
Fatigue 
o
10 100 1,000 10,000 100,000
Allowable 18 Kip Equivalent Load Applications, N x 10
3
FIGURE 0.7
SAMPLE OVERLAY THICKNESS DESIGN CURVES
vertical subgrade strain (€ ) for example.
The more comprehensive vs model proposed by Treybig et al. (1978) warrants a closer look if it were to be related to the South African situation as were the other proposals and recommendations mentioned before.
This may all be incorporated in a proposed catalogue of overlay designs, which would be similar to the existing TRH4 (NITRR, 1985a).
In consideration of remaining life as a criterion for fatigue cracking, the consideration of cracking only leads to some uneconomical overlay proposals.
Anderson (1977) indicates that a 50 per cent remaining life for fatigue cracking should be a critical value.
The structural performance model by Molenaar (1983) attempts to be more economical by considering the structural value of the cracked asphalt layer.
It also offers better consideration of the use of other new materials like bitumenrubber.
In the final selection of the thickness of the proposed overlay for the critical strain parameter, the emphasis is on checking the other parameter again in order to ensure that the overlay does not shorten remaining life after overlay for the previously noncritical parameter value.
From Anderson's (1977) work it is obvious that this would be of particular importance with thin overlays on thin asphalt concrete layers.
The approach by Treybig et al. (1978) to plot overlay thickness for both criteria simultaneously in relation to remaining life gives a good graphical indication of such trends.
It has been stated that the selection of an overlay must be seen against the background of maintenance or rehabilitation management systems.
The models discussed for analysis are not always applicable to the South African situation.
It is therefore suggested that the recommendations in regard to pavement performance and structure were made in previous sections be extended .
to this area of overlay design in order to make the whole design procedure mechanistically sound.
This could easily be incorporated in the suggested catalogue of overlay designs, mentioned above.
In Appendix B it was mentioned that there exists a good correlation between the measurements of the CrackActivityMeter (CAM) and deflection basin parameters as measured with the Road Surface
Deflectometer (RSD).
The normal procedure of initial assessment according to the draft TRH12 (1983) guidelines are carried out on a typical cemented base pavement.
In the detailed assessment stage the question whether the cracks recorded on specific sections are active or not must then be addressed with confidence.
The new service of the NITRR where the CAM and the RSD are combined can then give the required information to make a sound decision in regards to .
the rehabilitation option.
Various cracks with related block sizes and degrees of severity are selected on such a section under investigation.
At the same point (crack) the CAM and RSD are set up and measurements are taken with the Benkelmanbeam truck travelling over the crack following the WASHO procedure.
The crack activity measurements are then ·correlated with various other parameters such as block size and deflection basin parameters (Rust, 1984).
This appendix therefore describes how such an analysis on the N4/3 was used to verify the rehabilitation option selected in terms of its crack attenuation.
The cemented base of N4/3 is cracked and urgently needs rehabilitation.
Crack movement measurements were taken in October (Rust,
1986) .
It was found that there exists sections of road where the crack movements are very high.
The block sizes were found to be relatively large.
This means that the crack movements are likely to increase as the block sizes break down to a smaller size.
The rehabilitation option that was selected is to overlay the existing pavement with a 100 mm G1 crushed stone base and 40 mm asphalt surfacing.
The analysis described in this technical note is to determine what the effectiveness of the overlay is to reduce crack movement.
In the analysis use was made of measured deflection basins and the correlation thereof with crack movement measurements.
This was followed with a mechanistic analysis of the rehabilitation
option to calculate the deflection basin and predicted crack movements.
On each of the measuring points of the CAM the deflection basin was also measured with the RSD.
The measurement of the wnole deflection basin with the RSD makes it possible to determine various deflection basin parameters.
The most common deflection basin parameters
(Rust. 1986) that can be calculated from RSD measurements are listed in Table 1.1 with their respective formula.
The maximum horizontal crack movements (HMAX) and the maximum vertical crack movements
(VETOT) in micrometers were correlated with various deflection basin parameters.
The results were as follows:
904,271* (MAX. DEFL)2,6  9,483E6*(SCI915)2,5
+
3,086E3*(SCI610)I,5  2,538E2*(Dl1)l,3
+
9,81*(SCI305)l,4
+
71.765
4931.765*(MAX.
DEFL)5.2
 l,813E12*(SCI915)5.1
+
4.312E8*(SCI610)3.6
+
1;65E3*(Dl1)1.9

1.887E3*(SCI305)1.9
+ 49.713
Where: SCI
=
Surface curvature index with the subscripts indicating the offset for deflection in mm.
Dl1
=
Deflection Index which is the difference in deflection at 127 mm and 305 mm.
MAX. DEFL
VETOT
=
Maximum deflection in mm.
=
Total vertical movement in micrometer.
The regression analysis indicate that VETOT correlated better with the deflection basin parameters than HMAX.
The reason for that can clearly be related to the relatively large block sizes (Rust, 1986).
The pavement structures as shown in Figure E.1
for the existing pavement and the rehabilitated pavement were analysed mechanistically with the computer program ELSYM5.
The input values are as indicated in the figure.
The stress directly on top of the cemented base was calculated before and after the G1 crushed stone base overlay.
The calculated vertical stress was 374 kPa and after the overlay it was reduced to 111 kPa.
This is a drastic reduction in the calculated stress values and clearly indicates that the overlay did indirectly reduce the possible crack movements.
During the mechanistic analysis the deflection basin was calculated for the two pavement structures.
In Table E.1
the relevant deflection basin parameters are indicated.
The deflection basin parameters on top of the old cemented base (now subbase) and on top of the overlayed pavement are shown.
Deflection basin parameters (mm)
MAX. DEFL SCI915 SCI610 SCI305
0,253
0,230
When comparing the deflection basin parameters calculated on the surface directly it is shown in Table E.1 that the overlay reduces the deflection basin parameters values drastically.
This reduction in the respective deflection basin parameter values are even more when the values calculated on top of the cemented base are compared.
2,4m
EXISTING
EXISTING 150 CI
3,7 m
I
I i EXISTING PAVEMENT
3,7m
3,7 m rI
I
<t.
EXISTING PAVEMENT
50 AC
150 C I
FIGURE E.!
REHABILITATION OPTION
ON N4 /3
The regression analysis described earlier were also used to calculate the respective predicted crack movements.
These results are shown in Table E.2.
The results in Table E.2 show that there is a drastic reduction in the vertical and the horizontal crack movements.
In the case of the vertical crack movements the reduction was more.
This vertical movement was the more severe case for crack movement due to the relatively large block sizes.
(a) The crack movements (HMAX and VETOT) were correlated with various deflection basin parameters as measured with the CAM and the RSD.
(b) The vertical stress calculated on top of the cemented base show a drastic reduction in values when compared with the vertical stress values calculated on top of the cemented subbase of the overlayed pavement.
This reduction indicates that there should be a reduction in crack movements too.
(c) The deflection basin parameters were calculated for the existing pavement and the overlayed pavement.
These calculated deflection basin parameters were used in the correlation relationships to determine the calculated crack movements.
There is a drastic reduction in the crack movements on top of the cemented base due to the overlay.
Odemark
IS
(1949) equivalent layer thickness concept is used as a simple method of approximation.
It enables the transformation of a multilayered system into a single layer with equivalent thickness.
The principle is that the equivalent layer has the same stiffness as the original layer, so as to give the same pressure distribution underneath the layer.
This concept of classifying a pavement with one number that represents more or less the bearing capacity of that pavement is clearly illustrated by Molenaar and Van Gurp (1980) and
Molenaar (1983). The typical South African pavement structures that were analysed in chapter 7 were also converted to the equivalent layer thickness.
The equivqlent layer thickness values calculated were then rlated to various distress determinants and fatigue life in order to evaluate this concept as a possible aid in the mechanistic rehabilitation design procedure.
2
Ll E.(lv)
= aE h.
]. E (Iv.) s ].
II
I].
~ I
3
L where a = 0,9 for flexible pavements h.
].
= thickness of layer i in m
E
E.
].
= elastic modulus of layer i in N/m2
= elastic modulus of subgrade in
Nlm
s v.
].
=
Poisson ratio of layer i
2
V s
=
Poisson ratio of subgrade layer with value equal to 0,35
=
Number of layers
Molenaar (1983) and Molenaar and Van Gurp (1980) analysed a typical threelayered pavement structure.
The typical flexible pavement
structures referred to in this Appendix differ from this threelayered system in the sense that the pavement structures are either four layered or fivelayered systems with a different standard wheel load and tyre pressure.
The bitumen base pavements analysed resemble these threelayered pavements most closely in terms of thickness of the bitumen bases.
Most of the typical flexible pavement structures analysed.
though, have thin asphalt surfacings
(S 40 mm).
In Figures F.l and F.2 typical relationships of H versus deflection e basin parameters, shape factor (Fl) and slope of deflection (SO) are shown as calculated for bituminous base pavements.
The purpose is to show that some deflection basin parameters like SO, R. SCI, BCI and BOI can discern between the various subgrade elastic moduli while others, such as F 1 , F2, S, A and
Q cannot.
In Figure F. 3 surface curvature index (SCI) is shown for bituminous and granular bases versus H.
In both cases SCI can discern between the various e subgrade effective elastic moduli.
The gradients for these functions of the bitumen base pavements correlate well with bitumen base pavements with three layers (SCI with r
=
500 mm) (Molenaar and Van
Gurp,
1980).
The gradients for the relationships of the granular base pavements though, are shallow and reflect a greater sensitivity to changes in H .
e
Flexible pavements in general were grouped together in Figure F.4 to show that H correlates well with vertical subgrade strain (e: ).
e vs
The various values of effective elastic moduli of the subgrade lead to different relationships as shown in Figure F.4.
In Figure F. 5 the other distress determinant, horizontal asphalt tensile strain
(e: HA) , at the bottom of the bituminous base, is shown versus He'
Here again, there is a clear discernment between the elastic moduli of the subgrade.
It is however not possible to develop the same relationship between e: HA and He for the thin surfacings of granular base pavements.
One of the reasons for the latter situation seems to be that the thickness, Poisson ratio and elastic modulus ratio of the thin surfacing, compared to that of the base and even subgrade, differ markedly from that of a bituminous base pavement.
This is
<t
J:
CJ) a::
0
I
U
~
IJ..

0,5
0,2
0,1
0, I 0,2 0,5 t
2 5
EQUIVALENT LAYER THICKNESS (He) (m)
10
FIGURE F. I
EQUIVALENT LAYER THICKNESS VERSUS SHAPE
FACTOR F!
CJ)
CD
I
0
.;t en
0 to
(\J
10
I
.;t
0 en
Z
0
I
U
W
...l
IJ..
W
0
IJ..
0
CJ)
10
0,I 0,2 0,5 I 2 5
EQUIVALENT LAYER THICKNESS (He)(m)
FIGURE F.2
EQUIVALENT LAYER THICKNESS VERSUS SLOPE
OF DEFLECTION
tj
U')
E
E
10
0
I'f)
II
•..


E
::L
100
I
GRANULAR BASES
~
'"
"
"'
~
~
~
""'lIl
~
~
'" lC"""

I Es = 50 MPa
~
Es = 70 MPa
~
Es = 150 MPa
"'"
....•
~ ~~
~,.
~
~
~
BITUMEN BASES
\
~
\
~
.\
~
1\\
\~.
Es=50MPa
Es=70 MPa
Es= 150 MPa
..
\
\
~
'
,
1\
~
\ \
,
,
,
"
\~\
\
"
,\
.
10
0,3
EQUIVALENT
I 2
LAYER THICKNESS (Hel (ml
FIGURE
F.3
Equivalent layer th i ckness versus surface curvature index
I o
'f
~ut o to
I
~
.0
111
.•...
....
z
~ 500
~
(J)
I
::i..
100
0,3 I
EQUIVALENT LAYER THICKNESS (HeJ (m)
2
FIGURE F.4
VERTICAL SUBGRADE STRAIN VERSUS
EQUIVALENT LAYER THICKNESS FOR
FLEXI BLE PAVEMENTS
~ 100
<t
Q:
I
(/l
I
::t
E s
=
50 MPo
E s
=
70 M Po
Es =150 MPo
10
O,~____
EQUIVALENT
I 2
LAYER THICKNESS (HeHml
FIGURE F.5
EQUIVALENT LAYER THICKNESS VERSUS
MAXIMUM ASPHALT STRAIN FOR
BITUMEN BASE PAVEMENTS
clear when one looks at the formula for the calculation of H • given e
Equivalent layer thickness (H ) can be used to indicate whether a e pavement structure with cemented subbases or bases is in the flexible state, with the cemented layers in the cracked phase exhibiting equivalent granular behaviour according to the definition given by
Freeme (1983).
In Figure F.6, H for the precracked life of e pavements with cemented subbases and bases is shown in terms of standard 80 kN axle repetitions (E80s) determined as prescribed by
Freeme et al.
(l982a).
A distinction can be made based on the variance of the elastic modulus of the subgrade.
It can be seen, however, that an H value of at least 1,1 m is required for a e subgrade modulus of 70 MPa to have any significant precracked life of cemented layers.
This is rather high and reaffirms that the major portion of the structural life of typical TRH4 (NITRR, 1985a) pavement structures with cemented layers is in the cracked phase or flexible behaviour state.
The recommended vertical subgrade strain (e ) criteria for diffevs rent road categories (Freeme et al., 1982a) were used to calculate the standard 80 kN axle repetitions for all the flexible pavement structures for their respective values of H.
This relationship e between He and E80s is shown in Figure F.7 for all flexible pavement structures.
In this figure the fatigue life of bitumen base pavements was also calculated with respect to maximum asphalt strain
(eRA) and correlated with the respective He value.
The recommended fatigue life criteria for thick bitumen base pavements were used in th 1 1 t· e ca cu a J.on
(Freeme et al., 1982a).
The recommended shift factors shown in Table F.1 were applied to the calculated fatigue lives.
'0 m
~
"'
CD o
II')
I q
I o
'f'
Q'I
IJJ
0
CD

Ul
~ u
« a:: u
IJJ a::
Cl.
IJJ
...J
X
« z
..lie:
0
CD
0 a::
«
0 z
«
~
CJ)
CJ)
Z
0
!::
~
IJJ
Cl.
IJJ a:: 105
104
E s
50 MPo
70 MPo
150 MPo'" j
103
0,20
EQUIVALENT
1,0 5,0
LAYER THICKNESS (He) (m)
FIGURE F.G
Initiation of cracking of cemented bases and su bbases in terms of equivalent layer thickness
to

I
V
I o
V
"""en
0
CO
W
C/) z
0
I
~
W
Cl.
W
0::
107
I
E3


_
I
E vs
I
FORI
FLEXIBLE
PAVEMENTS
I I
I
I
I
I
TRH4 (NITRR 19850
TRAFFIC CLASSES
I t
 E4


W
...J
X
« a
0::
« a z
«
I
C/)
106
I
E2
r
I
,.,.
"'s
= 70
MPo
~EI
~
EO
105
0,1
EQUIVALENT
J

EHA FOR
BITUMEN
BASE
PAVEMENTS
1,0
LAYER THICKNESS(He) (m)
FIGURE F.7
Pavement life for maximum asphalt strain and vertical subgrade strain criteria in terms of equivalent layer thickness
The equivalent layer thickness (H ) concept proved to be a concept e that more or less represents the structural capacity of flexible pavements.
Deflection basin parameters correlate well with a value such as H in general, as calculated for flexible pavements.
It is e however only such deflection basin parameters, that normally use points of deflection near each other in the calculation procedure
(e.g.
scr,
R, BCI, BDI and SD), that can discern the effect of variance in subgrade elastic moduli.
Such relationships however do not have much value except as for an interim step towards establishing relationships between the distress determinants (£RA and £VS) and H .
e
He correlates well with subgrade vertical strain (£VS) for flexible pavement structures and discerns the effect of variance of subgrade elastic moduli.
Granular bases on the other hand do not give any clear relationships between maximum asphalt strain (£RA) and He as is the case with bitumen base pavements.
The reason seems to be the ratios of the thickness, elastic modulus and Poisson ratio of the surfacing and the base as well as that of the subgrade, in the calculation of· H , which leads to this marked difference between e granular and bitumen bases.
The value of H can be used in a mechanistic design or analysis e procedure to establish the structural life of a flexible pavement with regard to the distress determinants (£VS and £RA)' The precracked life of a cemented base and subbase layer can be determined.
It must be remembered though, that in order to use H in such a way, e the effective elastic moduli of all the layers as well as the thicknesses have to be known.
This restricts H to an interim value e in the determination of the distress determinants (£VS and £RA) in the mechanistic analysis of a pavement.
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Parameter
I.
Maximum deflection
2.
Radius of curvature
3.
Spreadability
4.
Area
5.
Shape factors
6.
Sur face curvature index
7.
Base curvature index
8. Base damage index
9.
Deflection ratio
10. Bending index
II. Slope of deflection
12. Tangent slope
13. Radius of influence
Formula
R
S
A
F
SCI
80
=
:: r
2
280 ( 80/8 r  \) i r
=
127 mm
[( 80+81+82+
8
3
)/5]
100 .
,
81""8
3 spaced
80
305mm
=
6[1+
2 (SI/80)
+2(8
2
/801"8
3
/80]
=
(80 82)
I
81
;
F
2
= (
8, 83)
18
2
=
8 o
':8 r
, r
=
305 or
500 mm
BCI
BDI
Or
BI
=
8610 8915
=
8305 8610
=
8r/80
, where
8 r ~ 80/2
=
80/a
, where a
= deflection basin length
SO
= tan
1
(808r
)/r
; where r
=
610 mm
ST
=
(8
o
8d/r .
, where r
= distance to inflection poi nt
RI
=
R'/8
0
) where
R
I is the distance from
80 to whe re basin is tangent to hori zontal.
a or
R'
Deflection basin length
Deflected / shape of road surface
Positive curvature
P
~Point of inflection
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